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A MANUAL 

OF 

THE PRINCIPLES AND PRACTICE 

OP 

O A D-M A K I N G 

COMPRISING 

THE LOCATION, CONSTRUCTION, AND IMPROVMENT 

OF 

ROADS, 

(COMMON, MACADAM, PAVED, PLANK. ETC.) 
AND 

RAIL-ROADS. 



W. M.'^ GILLESPIE, A. M., C. E. 

PROFESSOR OF CIVIL ENGINEERING IN UNION COLLEGl 
SIXTH EDITIOINT, WITH ADDITIONS. 



"Every judicious improvement in tlie establistiinent of Roads and bridges 
increases ttie value of land, enhances tlie price of cominodities, and augments 
tlie public wealth." Dk "Witt Clinton, 



NEW YORK 
PUBLISHED BY A. S. BARNES & CO. 

51 JOHN-STREET. 
1853. 



Entered, according to the Act of Congress, in the year 1847, by 

WILLIAM MITCHELL GILLESPIE. 

In the Clerk's Office of the District Court of the United States for the Southern 
District of New York. 



1 -^ 

f f 



^ 



r 77 



PREFACE. 



The common roads of the United States are inferior to those 
of any other civilized country. Their faults are those of direc- 
tion, of slopes, of shape, of surface, and generally of defi- 
ciency in all the attributes of good roads. Some of these 
defects are indeed the unavoidable results of the scantiness 
of capital and of labor in a new country, but most of them arise 
from an ignorance either of the true principles of road-making, 
or of the advantages of putting these principles into prac 
tice. They may therefore be removed by a more general difFu- ' 
sion of scientific instruction upon this subject, and to assist in 
bringing about this consummation is the object of the present 
volume. In it the author has endeavored to combine, in a 
systematic and symmetrical form, the results of an engineer- 
ing experience in all parts of the United States, and of an 
examination of the great roads of Europe, with a careful di- 
gestion of all accessible authorities, an important portion of 
the matter having never before appeared in English. He has 
striven to reconcile the many contradictory theories and 
practices of road-making ; to select from them those which 
are most in accordance with the teachings of science ; to 
present as clearly and precisely as possible the leading fea- 
tures of those approved, laying particular stress on such as 
are most often violated or neglected ; and to harmonize the 
successful but empirical practice of the English engineers 
with the theoretical but eleo;ant deductions of the French. 



4 PREFACE. 

Before the construction of a road is commenced, its makers 
should well determine " What it ought to ie," in the vital 
points of direction, slopes, shape, surface and cost. This is 
therefore the first topic discussed in this volume. The next 
is the "Location" of the road, or the choice of the ground 
over which it should pass, that it may fulfil the desired 
conditions. In this chapter are given methods of perform- 
ing all the necessary measurements of distances, directions 
and heights, without the use of any instruments but such as 
any mechanic can make, and any farmer use. The " Con- 
struction" of the road is next explained in its details of Exca- 
vation, Embankment, Bridges, Culverts, &c. At this stage 
of progress our road-makers too generally stop short, but the 
road should not be considered complete till " The Improve- 
ment of its surface" has been carried to as high a degree of 
perfection as the funds of the work will permit. Under this 
head are examined earth, gravel, McAdam, paved, plank and 
other roads. " Rail-roads," and their motive powers, are 
treated of in the next chapter. The " Management of town 
roads" is last taken up, the evils of the present system of 
Road-tax are shown, and a better system is suggested. In 
the " Appendix" are minute and practical examples of the 
calculations of Excavation and Embankment. 

To enable this volume the better to attain its aim of being 
doubly useful, as a popular guide for the farmer in improving 
the roads in his neighborhood, and as a College Text-book, 
intioductory to the general study of Civil Engineering, the 
mathematical investigations and professional details have been 
printed in smaller type, so as to be readily passed over by 
the unscientific reader. 

Tlie Tried Edition contained thirty additional pages, giving the practical details of 
the construction of Flmi,k Moods (pages 230 to 253), and the results of the latest ex- 
periments on the Resistances upon Railroads, on Curves, Ascents, &c. (pp. 264-278.) 

The present Edition has received such corrections and additions as were needed to 
bring its information up to the present moment, particularly with respect to Plank 
Eoads and Railroads. 

A Supplement to this volume, embracing many important points (Eailroad-location, 
Locomotives, &c.), too extensive to be inserted in the text, is in preparation. 



AUTHORITIES REFERRED TO. 



Alexander. Amer. Ed. of Simms on Levelling, Baltimore, 1837 

Annales des Fonts et Chauss^es, Faris. 

Anselin. Experiences sur la main-d'oeuvre des differens travaux, Faria. 

Babbage. Economy of Machinery and Manufactures, London, 183L 

Berthault-Ducraux. De I'Art d'entretenir les Routes, Faris, 1837. 

Bloodgood. Treatise on Roads, Albany, 1838. 

Chevalier. Les voies de communication aux Etats Unis, Faris, 1843 

Civil Engineers' and Architects' Journal, London. 

Cresy. Encyclopedia of Civil Engineering, London, 1847. 

Davies. Elements of Surveying, &c.. New York, 1845. 

Delaistre. La Science des Ingenieurs, Faris, 1825. 

Dupin. Applications de Geometrie, Faris, 1822. 

" Travaux civils de la Grande Bretagne, Faris, 1824. 
Eaton. Surveying and Engineering, Troy. 
Edgeworth. Construction of Roads and Carriages. 
Flachat ^ Bonnet. Manuel et Code des Routes et Chauss€es, Paris. 
Frome. Trigonometrical Surveying, London, 1840. 
Gayffier. Manuel des Fonts et Chaussees, Paris, 1844. 
Gerstner. Memoire sur les grandes routes, Faris, 1827. 
Grieg. Strictures on Road-police, London. 
Griffith. On Roads, London. 
Hughes. Making and Repairing Roads, London. 
Journal de I'Ecole Poly technique, Paris. 
Journal of the Franklin Institute, Philadelphia. 
Jullien. Manuel de I'lngenieur Civil, Paris, 1845. 
Laws of Excavation and Embankment on Railways, London, 1840. 
Lecount. Treatise on Railways, London, 1839. 

Macneill. Tables for calculating Cubic quantities of Earthwork, London. 
Mahan. Course of Civil Engineering, New York, 1846. 
Marlette. Manuel de I'Agent-voyer, Paris, 1842. 
McAdam. System of Road-Making, London, 1825 



5 AUTHORITIES. 

Millington. Civil Engineering, Philadelphia, 1839. 

Morin. Aide-Memoire de Mecanique, Paris, 1843. 

Mosely. Mech. principles of Engineering and Architecture, London, 1843 

Navier. Travaux d'entretien des Routes, Paris, 1835. 

" Application de la Mecanique aux constructions, Paris. 

Nimmo. On Roads of Ireland, &c. 
Parnell. Treatise on Roads, London, 1838. 

Paterson. Practical Treatise on Public Roads, &c., Montrose, 1£20. 
Penfold. On Making and Repairing Roads, London, 1835. 
Poncelet. Mecanique Industrielle, Paris, 1841. 
Potter. Applications of Science to the Arts, New York, 1847. 
Railroad Journal, New York, 1832-1847. 
Renwick. Practical Mechanics, New York, 1840. 
Reports of U. S. Commissioner of Patents, Washington. 
Reports of U. S. Engineer Corps, Washington. 
Reports to Parliament on Holyhead roads, &c., London. 
Ritchie. Railways, London, 1846. 
Road Act of New York, Rochester, 1845. 
Roads and Railroads, London, 1839. 
Sganzin. Course of Civil Engineering, Boston, 1837. 

" Cours de Construction par Reibell, Paris, 1842. 

Simnis, Telford's rules for making and repairing roads, London. 

" Public Works of Great Britain, London. 

" Sectio-Planography, London. 

Stevenson. Civil Engineering of North America, London, 1833< 
Telford. Reports on Holyhead roads, London. 
Tredgold. On Railroads, London, 1835. 
Wood. On Railroads, Philadelphia, 1832. 



ANALYTICAL TABLE OF CONTENTS. 



Page 

Introduction 15 

CHAPTER I.— WHAT ROADS OUGHT TO BE-- 25 

1. AS TO THEIR DIRECTION 26 

Importance of straightness ib 

Advantages of curving ib. 

Pleasure drives 30 

S. AS TO THEIR SLOPES 32 

Loss of power on inclinations ih. 

Undulating roads. • 37 

Greatest allowable slope 38 

Considered as a descent ih. 

" an ascent 40 

Least allowable slope 43 

Tables of corresponding slopes and angles 44 

3. AS TO THEIR OROSS-SEOTION 45 

Width ib. 

Shape of the road-bed 48 

Foot-paths, &c 53 

Ditches. ib. 

Side-slopes of the cuttings and fillings 55 

4. AS TO THEIR StTRFACE 58 

Qualities to besought ib. 

Smoothness and hardness ib. 

Resistances to be lessened ib. 

Elasticity ib. 

Collision 59 

Friction 60 



8 CONTENTS. 

_ Page 

5. AS TO THEIR COST 65 

Comparison of cost and revenue ib. 

Amount of Traffic 66 

Cost of its transportation ib. 

Profit of improving the surface 67 

" " lessening the length 68 

" " avoiding a hill ib. 

Consequent increase of travel 70 

CHAPTER II.— THE LOCATION OF ROADS 72 

1. AERAiraEMENT OF HILLS, VALLEYS AND WATEK- 

COUESES 74 

Line of greatest slope 75 

Inferences from the water-courses 78 

2. RECONNAISSANCE 81 

3. SURVEY OF A LINE 86 

Measurement of distances 87 

" directions 90 

" heights 93 

4. MAPPING THE SURVEY • 101 

Plot of the distances and directions ib. 

Profile of the distances and heights 103 

5. ESTABLISHING THE GFJIDES 105 

6. CALCULATING EXCAVATION AND EMBANKMENT 112 

Preliminary arrangements 113 

Seclio-FIanography ib. 

Tabular entries 115 

Cubical contents 117 

Balancing the excavation and embankment 118 

Shrinkage ; »*• 

Change of grade 119 

Transverse balancing. 123 

Distances of Transport 123 

7i ESTIMATE OF THE COST..... 124 

Earthwork *&• 

Wages '*• 

auality ^~5 

Distance ; ' ^~' 

Land, Bridges, (fee 132 



CONTENTS. y 

Paok 
8. FINAL LOCATION OF THE LDTE 134 

Rectification 135 

Curves 137 

Circular arcs 138 

Parabolic arcs. 143 

Setting grade pegs *145 

Stakmg out the side-slopes 145 



CHAPTER III.— CONSTRUCTION OF ROADS-.U? 

2. EARTHWORK 149 

Problems on removing earth ib. 

Excavation 1 54 

Loosening 26. 

Scraper or scoop 155 

Barrow wheeling 156 

Carts, etc 158 

Deep cuttings 159 

Spoil banks 160 

Side-slopes ib. 

Tunnelling 161 

Blasting ib. 

Embankments 1 65 

Formation of banks ib. 

Protection of slopes 167 

Swamps and bogs 163 

Side-hills 169 

Trimming and shaping 171 

2. MECHANICAL STRUCTURES 173 

Bridges ib. 

Culverts and drains 178 

Catchvvaters, or Water-tables 180 

Retaining Walls 182 



CHAPTER IV.— IMPROVEMENT OF THEIR 

SURFACE 188 

1. EARTH ROADS 189 

How to improve them ib. 

Effects of wheels on their surface 191 

2. GEAVELROADS 193 

Directions for their construction 16 



s 



10 CONTENTS. 

_ FA.OE 

3. BROKEN-STONE ROADS 194 

McAdam roads fj. 

Fundamental principles 195 

Quality of the stone 196 

Size of the broken stones - 198 

Breaking them 199 

Thickness of the coating. 200 

Application of the materials 201 

Rolling the new road 204 

Keeping up the road 205 

Kepairingit 209 

Telford roads 210 

Specification a. 

Propriety of a pavement foundation 212 

Foundation of concrete 215 

4i PAVED ROADS 216 

Pebble pavements ih. 

Squared stone pavements 217 

Foundations 218 

Of sand. ib. 

Of broken stones 219 

Ofpebbles ib. 

Ofconcrete - ib. 

Quality of stone 220 

Size and shape 221 

Arrangement. 222 

Manner of laying 223 

Borders and curbs 224 

Advantages 225 

Paved and McAdam roads compared ib. 

Roman roads 226 

6. ROADS OF WOOD 228 

Logs ih. 

Charcoal 229 

Plank 230 

Blocks 254 



CONTENTS. 1 1 

Page 

6. ROADS OF OTHER MATERIALS 255 

Bricks ib. 

Concrete ib. 

Cast iion ib. 

Asphaltum 256 

Caoutchouc ib, 

7. ROADS WITH TRACKWAYS 257 

Of stone ib. 

Of wood 259 

Of iron..... 260 



CHAPTER v.— RAIL-ROADS 261 

I. What Rail-roads ought to be • 264 

1. AS TO THEIR DIRECTION 2*70 

Economy of straightness ib. 

Evils of curves 2*71 

2. AS TO THEIR GRADES • 276 

Loss of po-wer on ascents ib. 

Compensating power of descents 280 

3. AS TO THEIR CROSS-SECTION 282 

The broad and narrow gauge question ib. 

Advantages of the broad gauge 283 

Objections to it 284 

The break of gange 285 

Width of road-bed 288 



II. The Location op Rail-eoads -290 

III. The Construction op Rail-roads •••• 291 

1. FORMING THE ROAD-BED...... ih. 

Excavations ib. 

Tunnels 292 

Embankments 293 

Ballasting 294 

Bridges and viaducts 295 



< 



12 CONTENTS. 

Paok 
2. THE SUPERSTRtTCTURE 297 

Rails supported at intervals ib. 

Their shape.. ?'J. 

Their weight ib. 

The distances of their suijporta ib. 

Theii- end joints 300 

Theirchairs 301 

Stone bloclis 303 

Wooden cross-sleepers 304 

Bails on continuous supports 305 

Inclination of the rails 308 

Elevation of the outer rail ib. 

Sidings, crossings, &c 309 

Single rail railroad 311 

IV. The Motive powers of Rail-roads 312 

1. HORSEPOWER. ib. 

Table of power at different speeds ib. 

2. STATIONARY ENGINES 313 

A Broadway railroad 314 

3. LOCOMOTIVB ENGINES 316 

History ib. 

Principles 321 

Speed and power 324 

"Working expenses 326 

Safety of travelling 328 

Signals 331 

4. ATMOSPHERIC PRESSURE 334 

History of its application ib. 

Description of present system, 335 

Advantages 338 



CONTENTS. 13 



Page 

CHAPTER VI.— THE MANAGEMENT OF TOWN 

ROADS 341 

The present Road-tax system 342 

Its defects 343 

New system proposed 345 



APPENDIX. 

Calculations of Excavation and Embankment^ 349 

1. By averaging end areas 350 

EiTor in excess 351 

2. By the middle areas 354 

Error in defect.-.. 355 

3. By the Prismoidal formula ib. 

Proof of its correctness 356 

Easier rules 357 

Formula for a series of equal distances 360 

Explanation of Tables 363 

4. By mean proportionals • 364 

5. Calculation of in-egular cross-sections ib. 

Their mean heights 367 

6. Tables for calculating Earth-work 369 

Slopes H to 1; Base 20 ib. 

« « Base30 370 

Slopes 2 to 1; Base 20 371 

« « BaseSO 373 



MANUAL OF ROAD-MAKING. 



INTRODUCTION. 



The Roads of a country are accurate and certain tests 
of the degree of its civilization. Their construction is 
one of the first indications of the emergence of a people 
from the savage state ; and their improvement keeps pace 
with the advances of the nation in numbers, wealth, in- 
dustry, and science — of all which it is at once an element 
and an evidence. 

Roads are the veins and arteries of the body politic, 
for through them flow the agricultural productions and the 
commercial supphes which are the life-blood of the state. 
Upon the sufficiency of their number, the propriety of 
their directions, and the unobstructedness of their courses, 
depend the ease and the rapidity with which the more 
distant portions of the system receive the nutriment which 
is essential to their life, health, and vigor, and without a 
copious supply of which the extremities must languish 
and die. 

But roads belong to that unappreciated class of bless- 
ings, of which the value and importance are not fully felt, 
because of the very greatness of their advantages, which 
are so manifold and indispensable, as to have rendered 
their extent almost universal and their origin forgotten. 
Perhaps we will better appreciate them, if we endeavor to 



16 A MANUAL OF ROAD-MAKING. 

imagine what would be our condition if none had ever 
been constructed. 

Suppose, then, that a traveller had occasion to go from 
Boston to Albany, and that no road between the two 
places was yet in existence. In the first place, how would 
he find his way ? Even if he knew that his general di- 
rection should be towards the setting sun, the sun would 
be often hidden by day, and the stars by night ; and, there 
being no roads, there would be no engineers and no sur- 
veyor's compass. The moss upon the north side of the 
trees might be in some degree a guide to him, if he were 
skilled in woodcraft ; but he would at last become so be- 
wildered, that, like lost hunters on the prairies, he would 
begin to beheve that the sun rose in the west, set in the 
east, and was due north at mid-day. 

Allowing, however, that he was fortunate enough to 
retain the true direction, would he be able to follow it '' 
In the forest he must force for himself a passage through 
the tangled underwood, and make long circuits around the 
fallen trees, which no axe-men have as yet cleared away. 
Through the swamp he must struggle amid the slippery 
and deceitful mud, for no road-maker has yet built the 
causeway. Over the mountain he must clamber only to 
again descend, for topographical science has not taught 
him how much he would gain by winding around its base. 
The rocky walls of precipices he must arduously climb, 
and perilously descend, for no engineer has as yet blasted 
a passage through them. Meeting a deep river, or even 
a mere mountain torrent, if he cannot ford or swim it, he 
must seek its head with many miles of added travel, to be 
doubled again by his return to his original direction. All 
this while, too, he can subsist only by precarious hunting ; 
for, there being no roads, there would be no inns, and 



INTRODUCTION. 17 

he can scarcely carry himself along, much less a store of 
provisions. 

Look now at the contrast, and at the ease, speed, and 
comfort with which the modern traveller flies from place 
to place upon that best of all roads, a railroad. 

But the increase of personal comfort is only a petty 
item in estimating the importance of roads, even in despite 
of Dr. Johnson's exclamation, that life has no greater 
pleasure than being whirled over a good road in a post- 
chaise. More important is the consideration, that, in 
the absence of such facilities, the richest productions 
of nature waste on the spot of their growth. The lux- 
uriant crops of our western prairies are sometimes left 
to decay on the ground, because there are no rapid and 
easy means of conveying them to a market. The rich 
mines in the northern part of the state of New York are 
comparatively valueless, because the roads among the 
mountains are so few and so bad, that the expense of the 
transportation of the metal would exceed its value. So, 
too, in Spain, it has been known after a succession of 
abundant harvests, that the wheat has actually been al- 
lowed to rot, because it would not repay the cost of car- 
riage.* In that country, for similar reasons, sheep are 
killed for their fleece only, and the flesh is abandoned ; as 
is likewise the case with cattle in Brazil, slaughtered 
merely for their hides. 

Such are the effects of the almost total want of roads. 
Among those which do exist, the diflference, as to ease, 
rapidity, and economy of transportation, caused by the va- 
rious degrees of skill and labor bestowed upon them, is 
much greater than is usually imagined, particularly by 
farmers, whom they most concern. 

* Edinburgh Review, Ixv. 448. 
2 



18 A MANUAL OF ROAD-MAKINGr 

One important difference lies in the grades or longitu 
dinal slopes of a road. Suppose that a road rises a hun- 
dred feet in the distance of two thousand feet. Its ascend- 
ing slope is then one in twenty, and (as will be hereafter 
proven) one-twentieth of the whole load drawn over it in 
one direction, must be actually lifted up this entire height 
of one hundred feet. But upon such a slope a horse can 
draw only one half d.^ much as he can upon a level road, 
and two horses will be needed on such a road to do the 
usual work of one. If the road be intrusted to the care 
of a skilful engineer, and be made level by going round 
hills instead of over them, or in any other way, there will 
be a saving of one half of the former expense of carriage 
on it. 

Another great difference in roads lies in the nature of. 
their surfaces : one being hard and smooth, and another 
soft and uneven. On a well-made road of broken stone, a 
horse can draw three times as much as he can upon a 
gravel road. By making, then, such a road as the former 
(according to the instructions in Chapter IV.) in the place 
of the latter, the expenses of transportation will be re- 
duced to one-third of their former amount, so that two- 
thirds will be completely saved, and two out of three of all 
the horses formerly employed can then be dispensed with.* 
If such an improvement can be made for a sum of money, 
the interest of which will be less than the total amount of 
the annual saving of labor, it will be true economy to 
make it, however great the original outlay ; for the de- 

* In the absence of such an improvement, when the Spanish govern- 
ment required a supply of grain to be transferred from Old Castile to 
Madrid, 30,000 horses and mules were necessary for the transportation of 
480 tons of wheat. Upon a broken-stone road of the best sort, one-hun 
dredth of that number could easily have done the work. 



INTRODUCTION. 19 

cision of all such questions depends on considerations of 
comparative profit. This part of the subject will be more 
minutely examined at the end of Chapter 1., in considering 
" What roads ought to be as to their cost." 

The profits of such improvements are not confined to the 
proprietors of a road, (whether towns, or companies re- 
munerated for these expenditures by tolls) but are shared 
by all who avail themselves of the increased facilities ; * 
consumers and producers, as well as road-owners. If 
wheat be worth in a city a dollar per bushel, and if it 
cost 25 cents to transport it thither from a certain farming 
district, it will there necessarily command only 75 cents. 
If now by improved roads the cost of carriage is reduced 
to 10 cents, the surplus 15 cents on each bushel is so much 
absolute gain to the community, balanced only by the cost 
of improving the road. Supposing that a toll of 5 cents 
will pay a fair dividend on this, there remains 10 cents per 
bushel to be divided between the producer and the con- 
sumer, enabling the former to sell his wheat at a higher 
price than before, while at the same time the latter obtains 
it at a less cost. 

Agriculture is thus directly, and likewise indirectly, de- 
pendent in a great degree upon good roads for its success 
and rewards. Directly, as we have just seen, these roads 
carry the productions of the fields to the markets, and 
bring to them in return their bulky and weighty materials 
of fertilization, at a cost of labor which grows less and less 
as the roads become better. Indirectly/, the cities and 
towns, whose dense population and manufacturing indus- 
try make them the best markets for farming produce, 
are enabled to grow and to extend themselves indefinitely 
by roads alone, which supply the place of rivers, to the 
banks of which these great towns would otherwise be ne- 



20 A MANUAL OF RO A.D-MAKING. 

cessarily confined.* While, therefore, it would be an m 
excusable waste of money to construct a costly road to 
connect two small towns which had little intercourse, it 
would be equally wasteful, and is a much more frequent 
short-sightedness of economy, to leave unimproved and 
almost in a state of nature, the communications between 
a great city and the interior regions from which its daily 
I ' sustenance is drawn, and into which its own manufactures 
are conveyed. 

Some of the advantages thus to be attained, have been 
well summed up in a report of a committee of the House 
of Commons : 

" By the improvement of our roads, every branch ot 
our agricultural, commercial, and manufacturing industry 
would be materially benefited. Every article brought to 
market would be diminished in price ; and the number of 
horses would be so much reduced that, by these and other 
retrenchments, the expense of five millions [pounds 
sterling] would be annually saved to the pubhc. The 
expense of repairing roads, and the wear and tear of car- 
riages and horses, would be essentially diminished ; and 
thousands of acres, the produce of which is now wasted 
in feeding unnecessary horses, would be devoted to the 
production of food for man. In short, the public and 
private advantages which would result from effecting that 
great object, the improvement of our highways and turn- 
pike roads, are incalculable ; though, from their being 
spread over a wide surface, and available in various ways, 
such advantages v/ill not be so apparent as those derived 
from other sources of improvement, of a more restricted 
and less general nature." 

* McCulloch, Dictionary of Commerce. 



INTRODUCTION. 21 

The changes in the condition of a country which such 
improvements effect, are of the highest importance. There 
is as much truth as blundering in the famous couplet writ- 
ten by an enthusiastic admirer of the roads which Marshal 
Wade opened through the Scottish Highlands : 

" Oh, had you only seen these roads before they were made, 
You would lift up your eyes and bless Marshal Wade !" 

His military road is said to have done more for the civili- 
zation of the Highlands than the preceding efforts of all 
the British monarchs. But the later roads under the more 
scientific direction of Telford, produced a change in the 
state of the people which is probably unparalleled in the 
history of any country for the same space of time. Large 
crops of wheat now cover former wastes ; farmers, houses, 
and herds of cattle are now seen where was previously a 
desert ; estates have increased sevenfold in value and 
annual returns ; and the country has been advanced at 
least one hundred years. In Ireland similar effects have 
been produced, and the face of the country in some dis- 
tricts has been completely renovated. The enlarged labors 
of the public works, now undertaken in that country by 
the government, though commenced only for temporary 
relief, will not fail to produce great permanent benefits. 

The moral results of such improvements are equally 
admirable. Telford testifies that in the Highlands they 
greatly changed for the better the habits of the great 
working class. Thus, too, when Oberhn wished to im- 
prove the spiritual condition of his rude flock, he began 
by bettering their physical state, and led out his whole 
people to open a road of communication between their 
secluded valley and the great world without. The won- 
derful moral and intellectual amelioration which ensued 



22 - A MANUAL OF ROAD-MAKING. 

was an unmistakeable tribute to the civilizing and eleva- 
ting influence of good roads. 

Anaong the most remarkable consequences of the im- 
provement of roads, is the rapidly increasing proportion in 
which their benefits extend and radiate in every direction, 
as impartially and benignantly as the similarly diverging 
rays of the sun. Around every town or market-place we 
may conceive a number of concentric circles to be drawn, 
enclosing areas from any part of which certain kinds of 
produce may be profitably taken to the town ; while from 
any point beyond each circumference, the expense of the 
carriage of the particular article would exceed its value. 
Thus the inner circle, at the centre of which is the town, 
may show the limit in every direction from beyond which 
perishable vegetables, or articles very bulky or heavy in 
proportion to their value, cannot be profitably brought to 
market ; the next larger circle may show the limit of 
fruits ; and so on. If now the roads are improved in any 
way, so as in any degree to lessen the expense of car- 
riage, the radius of each circle is correspondingly in- 
creased, and the area of each is enlarged as the square of 
this ratio of increase. Thus, if the improvement enables 
a horse to draw twice as much or to travel twice as fast 
as he did before, each of the limiting circles is expanded 
outward to twice its former radius, and embraces foui 
times its former area. If the rate of improvement be 
threefold, the increase of area is ninefold ; and so on 
All the produce, industry, and wealth, which by these im 
provements finds, for the first time, a market, is as it were 
a new creation.* 

The number of passengers is governed by similar laws ; 

* Dr. Anderson. 



INTRODUCTION, 23 

and the increased facilities of a better road attract them 
from inferior ones, as the digging of a new and deep well 
often drains the water from all the shallow ones in its 
neighborhood. The distance to the right and left of the 
new road, from which it will attract passengers, admits of 
a mathematical investigation, which will be found at the 
end of Chapter I. ; and the deductions of theory are amply 
corroborated by the observations of experience, and more 
than realized in the improvement of every old road and the 
opening of every new one ; for not only is the former 
travel attracted from great distances in every direction, 
but a very considerable amount is created. 

Supposing that by these improvements the average 
speed over a whole country be only doubled, the whole 
population of the country (to borrow a metaphor from an 
accomplished writer) would have advanced in mass, and 
placed their chairs twice as near to the fireside of their 
metropolis, and twice as near to each other. If the speed 
were again doubled, the process would be repeated; and so 
on. As distances were thus gradually annihilated, the whole 
surface of the country would be, as it were, contracted and 
condensed, till it was only one immense city ; and yet, 
by one of the modern miracles of science wedded to art, 
every man's field would be found not only where it always 
was, but as large as ever it was, and even far larger, esti- 
mating its size by the increased profits of its productions, 
The more perfect the roads, the more rapidly would this 
result be attained, and therefore most quickly of all by 
railroads. 

But however great the advantages of railroads, as to 
mere speed, and however precious to the hurrying travel- 
ler their triumphs over time and space, common roads will 
always be incomparably more valuable to the comm.unity 



^ 



24 A MANUAL OF ROAD-MAKING. 

at large. The distinguishing characteristic of a modern rail- 
road, as compared with a " tram road," and that to which 
its peculiar power is chiefly due, is the projecting flanges 
of the wheels of its carriages, by which they are retained 
upon the rails. But this pecuharity, in an equal degree, 
lessens its advantages to the agricultural population ; since 
the vehicles which are adapted to travel on railroads can- 
not be used on the common roads leading to them, nor in 
the ordinary labors of the farm ; while on all other im- 
proved roads the same wagons, horses, and men, employed 
at one season in cultivating the ground, can also be pro- 
fitably employed, in their otherwise idle moments, in con- 
veying the produce to a market. For these reasons, even if a 
railroad came to every man's door, he could more economi- 
cally use a good common road ; but since, on the con- 
trary, the expense of the construction of railroads must al- 
ways restrict them to important lines of communication, 
(where, indeed, their value can scarcely be estimated too 
highly) in every other situation, the greatest good of the 
greatest number, and the most universal benefits with the 
fewest accompanying evils, will be most effectually se- 
cured, by improving (in accordance wiih the principles 
to be presently set forth) the people s highways — the 
common roads of the country. 

In this analytical examination of the subject of Road- 
making, it will be considered under the ioiiowing general 
heads : 

1. What Roads ought to be. 

2. Their Location. 

3. Their Construction. 

4. Improvement of their Surface. 



CHAPTER I. 

WHAT ROADS OUGHT TO BE. 

" The art of Road-making must essentially depend for its success on 
its being exercised in conformity with certain general principles ; and 
their justness should be rendered so clear and self-evident as not to admit 
of any controversy." 

Sir Henry Farneix. 

Rapidity, safety, and economy of carriage are the ob- 
jects of roads. They should therefore be so located and 
constructed as to enable burdens, of goods and of passen- 
gers, to be transported from one place to another, in the 
least possible time, with the least possible labor, and, con- 
sequently, with the least possible expense. 

To attain these important ends, a road should fulfil cer- 
tain conditions, which the nature of the country over which 
it passes, and other circumstances, may render impossible 
to unite and reconcile in one combination ; but to the union 
of which we should endeavor to approximate as nearly as 
possible in forming an actual road upon the model of this 
ideally perfect one. We will therefore investigate — 

What roads ought to be, 

1. As to their direction. 

2. As to their slopes. 

3. As to their cross-section. 

4. As to their surface. 

5. As to their cost. 



26 WHAT ROADS OUGHT TO BE. 

1. WHAT KOADS OUGHT TO BE, AS TO THEIR DIEEOTIOM". 
IMPORTANCE OF STRAIGHTNESS. 

Every road, other things being equal, should be per- 
fectly straight, so that its length, and, therefore, the time 
and labor expended in travelling upon it, should be the least 
possible ; i. e., its alignemens, or directions, departing 
from one extremity of it, should constantly tend towards 
the other. 

Any unnecessary excess of length causes a constant 
threefold waste ; firstly, of the interest of the capital ex- 
pended in making that unnecessary portion ; secondly, of 
the ever-recurring expense of repairing it ; and, thirdly, of 
the time and labor employed in travelling over it. It will 
therefore be good economy to expend, in making topo- 
graphical examinations for the purpose of shortening the 
road, any amount less than not only that sum which the 
distance thus saved would have cost, but, in addition, that 
principal which corresponds to the annual cost of the re- 
pairs and of the labor of draught which would have been 
wasted upon this unnecessary length. 

ADVANTAGES OF CURVING. 

The importance of making the road as level as possible 
will be explained in the next section, and as a road can in 
few cases be at the same time straight and level, these two 
requirements will often conflict. In such cases, straightness 
should always he sacrificed to obtain a level, or to make 
the road less steep. This is one of the most important 
principles to be observed in laying out or improving a road, 
and it is the one most often violated. 

A straight road over an uneven and hilly country may, 
at first view, when merely seen upon the map, be pro- 



ADVANTAGES OP CURVING. 27 

nounced to be a had road ; for the straightness must have 
been obtained either by submitting to steep slopes in as- 
cending the hills and descending into the valleys, or these 
natural obstacles must have been overcome by incurring 
a great and unnecessary expense in making deep cuttings 
and fillings. 

A good road should wind around these hills instead of 
running over them, and this it may often do without at all 
increasing its length. For if a hemisphere (such as half 
a bullet) be placed so as to rest upon its plane base, the 
halves of great circles which join two opposite points of 
this base are all equal, whether they pass horizontally or 
vertically. Or let an egg be laid upon a table, and it will 
be seen that if a level line be traced upon it from one end 
to the other, it will be no longer than the line traced be- 
tween the same points, but passing over the top. Pre- 
cisely so may the curving road around a hill be often no 
longer than the straight one over it ; for the latter road is 
straight only with reference to the vertical plane which 
passes through it, and is curved with reference to a hori- 
zontal plane ; while the former level road, though curved 
as to the vertical plane, is straight as to a horizontal one. 
Both lines thus curve, and we call the latter one straight 
in preference, only because its vertical curvature is less 
apparent to our eyes., 

The difference in length between a straight road and 
one which is slightly curved is very small. If a road be- 
tween two places ten miles apart were made to curve so 
that the eye could nowhere see farther than a quarter of 
a mile of it at once, its length would exceed that of a 
perfectly straight road between the same points by only 
about one hundred and fifty yards.* 

* Sganzin, p. 89. 



28 WHAT ROADS OUGHT TO BE. 

But even if the level and curved road were very much 
longer than the straight and steep one, it would almost 
always be better to adopt the former ; for on it a horse could 
safely and rapidly draw his full load, while on the other he 
could carry only part of his load up the hill, and must di- 
minish his speed in descending it. 'As a general rule, the 
horizontal length of a road may be advantageously in- 
creased, to avoid an ascent, by at least twenty times the 
perpendicular height which is to be thus saved ; that is, to 
escape a hill a hundred feet high, it would be proper for 
the road to make such a circuit as would increase its 
length two thousand feet.* The mathematical axiom that 
" a straight line is the shortest distance between two 
points," is thus seen to be an unsafe guide in road- 
making, and less appropriate than the paradoxical proverb 
that '' the longest way around is the shortest way home." 

The gently curving road, besides its substantial advan 
tages, is also much more pleasant to the traveller upon it ; 
for he is not fatigued by the tedious prospect of a long 
straight stretch of road to be traversed, and is met at each 
curve by a constantly varied view. 

It cannot oe too strongly impressed upon a road-maker, 
that straightness is not the highest characteristic of a good 
road. As says Coleridge — 

" Straight forward goes 
The lightning's flash, and straight the fearful path 
Of the cannon-ball." 

But in striking contrast he adds — 

" The ROAD the human being travels, 
That on which blessing comes and goes, doth follow 
The river's course, the valley's playful windings, 
Curves round the cornfield and the hill of vines."t 

* This proportion depends on the degree of friction assumed, a subject 
to be investigated in a following section. 
t The Piccolomini. i, 4. 



DISADVANTAGES OF STRAIGHTNESS. 29 

The passion for straightness is the great fault in the 
location of most roads in this country, which too often 
remind us how 

" The king of France, with forty thousand men, 
Marched up a hill, and then — marched down again ;" 

SO generally do they clamber over hills which they could 
so much more easily have gone around ; as if their ma- 
kers, like Marshal Wade, had " formed the heroic deter- 
mination of pursuing straight lines, and of defying nature 
and wheel-carriages both, at one valiant effort of courage 
and of science." 

One reason of this is, that the houses of the first set- 
tlers were usually placed on hill-tops, (to escape the poi- 
sonous miasmata of the undrained swamps, and to detect 
the approach of the hostile savages) and that the first 
roads, necessarily ran from house to house. Our error 
consists in continuing to follow these primitive roads with 
our great thoroughfares. These original paths were also 
traversed only by men, and therefore very properly fol- 
lowed the shortest though steepest route. Tracks for 
pack-horses came next, and a considerable degree of 
steepness is admissible in them also. Wheeled carriages 
were finally introduced and brought into use upon the 
same tracks, though too steep for true economy of labor 
with them — the standard of slope being very different for 
foot, horse, and carriage roads. Before sufficient attention 
was paid to the subject, the lands on either side of the 
road had been fenced off and appropriated by individuals, 
and thus the random tracks became the legal highways. 

The evil is now perpetuated by the unwillingness of 
farmers to allow a road to run through their farms in a 
winding line. They attach more importance to the square- 



T 



30 WHAT ROADS OUGHT TO BE. 

ness of their fields than to the improvement of the lines 
of their roads — not being aware how much more labor is 
wasted by them in travelling over these steep roads, than 
there would be in cultivating an awkward corner of a 
field. 

This feeling is seen carried to excess in some of the 
new states of the West, in which the roads now run along 
" section-hnes," and as these sections are all squares, with 
sides directed towards the cardinal points of the compass, 
a person wishing to cross the country in any other direc- 
tion than North, South, East or West, must do so in rec- 
tangular zigzags. 

PLEASURE DRIVES. 

In roads designed solely for pleasure drives, such as 
those laid out by landscape gardeners in parks, cemeteries, 
&c., curvature is the rule, and straightness only the ex- 
ception. In them the object is to wind as much as possible, 
m Hogarth's " line of grace," so as to obtain the greatest 
development of length which the area of the ground will 
permit, but at the same time never to appear to turn for 
the mere sake of curving. Some reason for the windings 
must always be suggested, such as a clump of trees, a rise 
of ground, a good point of view, or any object which may 
conceal the artifice employed. The visiter must be de- 
ceived into the belief that he is travelling over a large area, 
while he is truly only retracing his steps and constantly 
doubling upon his track ; but he must do it unconsciously, 
or at least without knowing the precise manner in which 
the pleasant deception is effected. Ars est celare artem. 

The map on the opposite page, representing the roads 
and paths in Greenwood Cemetery, will somewhat illus- 
trate this principle. 



32 



WHAT ROADS OUGHT TO BE. 



2. WHAT ROADS OUGHT TO BE AS TO THEIR SLOPES. 

LOSS OF POWER ON INCLINATIONS. 

Every road should be perfectly level. If it be not, a 
large portion of the strength of the horses which travel it 
will be expended in raising the load up the ascent. When 
a weight is drawn up an inclined plane, the resistance of 
the force of gravity, or the weight to be overcome, is such 
a part of the whole weight, as the height of the plane is of 
its length If, then, a road rises one foot in every twenty 
of its length, a horse drawing up it a load of one ton is 
compelled to actually lift up one-twentieth of the whole 
weight, i. e., one hundred pounds, through the whole 
height of the ascent, besides overcoming the friction of 
the entire load. 



Fig. 2. 

Let DE re- 
present the in- 
clined surface 
of a road^ upon 
which rests a 
wagon, the cen- 
tre of gravity of 
which is sup- 
posed to be at 

C. Draw CA perpendicular to the horizon, and CB perpen- 
dicular to the surface of the hill. Let CA represent the force 
of gravity, or the weight of the wagon and its load. It is 
equivalent, in magnitude and direction, to its two rectangular 
component forces, CB and BA. CB will then represent the 
force with which the wagon presses on the surface of the road, 
and AB the resisting force of gravity, i. e., the force (inde- 




LOSS OF POWER ON INCLINATIONS. 



33 



pendent of friction) which resists the ascent of the wagon, or 
which tends to drag it down hill. 

To find the amount of this force, from the two similar tri- 
angles, ABC and DEF, we get the proportion 

CA : AB : : DE : EF. 

Representing the length of the plane by I, its height by h, 

and the weight of the wagon and load by W, this proportion 

becomes 

^^ : AB : : I : h, 

h 
whence AB=:W-r ; that is, the resistance of gravity due to 

the inclination, is equal to the whole weight, multiplied by the 
height of the plane and divided by its length. If the inclina- 
tion be one in twenty, then this resistance is equal to -^^ W, 

In this investigation, we have neglected three trifling sources 
of error : arising from part of the weight being thrown from 
the front axles to the hind ones, in consequence of the inclina- 
tion of the traces ; from the diminution of the pressure of 
the weight, owing to its standing on an inclined surface ; and 
from the hind wheels bearing more than half of the pressure, 
in consequence of the line of gravity falling nearer them. 

The results of experiments fully confirm the deductions 
of theory as to the great increase of draught upon incli- 
nations. The following table exhibits the force required 
(according to Sir Henry Parnell) to draw a stage coach 
over parts of the same road, having different degrees of 
inclination : 



Inclination. 


FORCE OF DRAUGHT REQUIRED. 


At 6 miles per hour. 


At 8 miles per hour. 


At 10 miles per hour. 


1 in 20 
1 in 26 
1 in 30 
1 in 40 
1 in 600 


268 

213 
165 
160 
111 


296 
219 
196 
166 
120 


318 
225 
200 
173 
128 



34 



WHAT ROADS OUGHT TO BE. 



Putting into a different form the results of these and other 
experiments, we establish the following data : 

Calling the load which a horse can draw on a level, 1.00 
on a rise of 1 in 100 a horse can draw only .90* 



1 in 50 


(1 (( 


.81* 


1 in 44 " 


(t (( 


.15% 


1 in 40 


(( (( 


.72t 


1 in 30 " 


(( (( 


.64t 


1 in 26 " 


U (( 


.54t 


1 in 24 


(( t( 


.50$ 


1 in 20 " 


U (( 


.40t 


1 in 10 " 


(( C( 


.25* 



In round numbers, upon a slope of 1 in 44, or 120 ieet 
lo the mile, a horse can draw only three-quarters as much 
as he can upon a level ; on a slope of 1 in 24, or 220 feet to 
the mile, he can draw only half as much ; and on a slope 
of 1 in 10, or 528 feet to the mile, only one quarter as 
much. 

This ratio will, however, vary greatly with the nature 
and condition of the road ; for, although the actual re- 
sistance of gravity is always absolutely the same upon the 
same inclination, whether the road be rough or smooth, 
yet it is relatively less upon a rough road, and does not 
form so large a proportional share of the whole resist- 
ance. 

Thus, if the friction upon a road were such as to require, 
upon a level, a force of draught equal to ^V of the load, the total 
force required upon an ascent of 1 in 20, would be 4V~l"2V^=4^o- 
Here, then, the resistance of gravity is two-thirds of the 
whole. 

If the road be less perfect in its surface, so that its friction 



* Gayffier. Experiments on a French road. 

+ Parnell. Experiments on an English road at average of Ihe three 
velocities. 

t Interpolations. 



LOSS OF POWER ON INCLINATIONS. 35 

=: Jg, the total force upon the ascent will be -^^ + ^V ? and 
here, then, the resistance of gravity is one-half of the whole. 

If the friction increase to ~, the total resistance is 
-i\-{-2\)^^'io '^ ^^^ here, gravity is only one-third of the whole. 

We thus see that on a rough road, with great friction, 
any inclination forms a much smaller part of the resist- 
ance than does the same inclination on a smooth road, on 
which it is much more severely felt, and proportionally 
more injurious ; as the gaps and imperfections which 
would not sensibly impair the value of a common knife, 
would render a fine razor completely useless. 

The loss of power on inclinations is indeed even greater 
than these considerations show ; for, besides the increase 
of draught caused by gravity, the power of the horse to 
overcome it is much diminished upon an ascent, and in 
even a greater ratio than that of man, owing to its ana- 
tomical formation and its great weight. Though a horse, 
on a level, is as strong as five men, yet on a steep hill it 
is less strong than three ; for three men, carrying each 
100 lbs., will ascend faster than a horse with 300 lbs.* 

Inclinations being always thus injurious, are particularly 
so, where a single steep slope occurs on a long line of 
road which is comparatively level. It is, in that case, 
especially important to avoid or to lessen this slope, since 
the load carried over the whole road, even the level por- 
tions of it, must be reduced to what can be carried up the 
ascent. Thus, if a long slope of 1 in 24 occurs on a level 
road, as a horse can draw up it only one half of his full 
load, he can carry over the level parts of the road only 
half as much as he could and should draw thereon. 

This evil is sometimes partially remedied by putting on 
a full load and adding extra horses at the foot of the steep 

* Emerson. Mechauics, 



3b WHAT ROADS OUGHT TO BK 

slope. Oxen are thus employed to assist carriages up the 
high hills, on the summits of which, for safely in time of 
war, the Etruscans built their cities of Perugia, Cortona, 
&c. But this is an inconvenient, as well as expensive 
system, and the truest economy is, to cut down, or to go 
around such acclivities, whenever this is possible.* 

The bad effects of this steepness are especially felt m 
winter, when ice covers the road, for the slippery surface 
causes danger in descending, as well as increased labor in 
ascending. The water of rains, also, runs down the road 
and gullies it out, destroying its surface, and causing a 
constant expense for repairs, oftentimes great enough to 
pay for a permanent improvement. 

The loss of power on inclinations being so great as has 
been shown, it follows that it is very important never to 
allow a road to ascend or descend a single foot more than 
is absolutely unavoidable. If a hill is to be ascended, the 
road up it should nowhere have even the smallest fall or 
descent, for that would make two hills instead of one ; but 
it should be so located and have such cuttings and fillings, 
as will secure a gradual and uninterrupted ascent the 
whole way. 

In this point engineering skill can make wonderful improve- 
ments. Thus, an old road in Anglesea, laid out in violation of 
this rule, rose and fell between its extremities, 24 miles apart, 
a total perpendicular amount of 3,540 feet ; while a new road 
laid out by Telford between the same points, rose and fell only 
2,257 feet ; so that 1,283 feet of perpendicular height is now 
done away with, which every horse passing over the road had 
previously been obliged to ascend and descend with its load. 
The new road is, besides, more than two miles shorter. Such is 

* In Chapter IV., under the head of " Roads with Trackways," will be 
described a valuable palliation of the evils of steep ascents in cases where 
they cannot be avoided. 



UNDULATING ROADS. 37 

one of the results of the labors of a skilful road-maker, and many 
such improvements might be made in onr American roads. 
For a recent remarkable instance, see page 233. 

UNDULATING ROADS. 

There is a popular theory that a gently undulating road 
is less fatiguing to horses than one which is perfectly level. 
It is said that the alternations of ascent, descent, and levels, 
call into play different muscles, allowing some to rest while 
the others are exerted, and thus relieving each in turn. 

Plausible as this speculation appears at first glance, it 
will be found on examination to be untrue, both me- 
chanically and physiologically ; for, considering it in the 
former point of view, it is apparent that new ascents are 
formed which offer resistances not compensated by the 
descents ; and in the latter, we find that it is contradicted 
by the structure of the horse. The question was submitted 
by Mr. Stevenson* to Dr. John Barclay of Edinburgh, 
"no less eminent for his knowledge, than successful as 
a teacher of the science of comparative anatomy," and 
he made the following reply : — " My acquaintance with 
the muscles by no means enables me to explain how a 
horse should be more fatigued by travelling on a road uni- 
formly level, than b)r travelling over a like space upon one 
that crosses heights and hollows ; but it is demonstrably 
a false idea, that muscles can alternately rest and come 
into motion in cases of this kind Much is to be as- 
cribed to prejudice originating with the man, continually 
in quest of variety, rather than with the horse, who, con- 
sulting only his own ease, seems quite unconscious of 
Hogarth's Line of Beauty." 

Since this doctrine is thus seen to be a mere popular 

* Report on the Edinburgh Railway. 



38 WHAT ROADS OUGHT TO BE. 

error, it should be utterly rejected, not only because false 
in itself, but still.more because it encourages the making 
of undulating roads, and thus increases the labor and cost 
of carriage upon them. 

GREATEST ALLOWABLE SLOPE. 

A perfectly level road is thus seen to be a most desira 
ble object ; but as it can seldom be completely attained, 
we must next investigate the limits to which the slopes of 
a road shotdd be reduced if possible, and determine what 
is the steepest allowable or maximum slope. 

This depends on two different considerations, according 
as the slope is viewed as a descent or as an ascent, each 
of which it alternately becomes, according to the direction 
of the travel. ' 

Viewed as a descent, it chiefly concerns the safety ot 
rapid travelhng, and applies especially to great public 
roads. 

Viewed as an ascent, it chiefly concerns the draught of 
heavy loads, and relates particularly to routes for agricul- 
tural and other heavy transportation. 

MAXIMUM SLOPE, CONSIDERED AS A DESCENT. 

The slope should be so gentle, that when a heavy ve- 
hicle is descending, its gravity shall not overcome its 
friction so far as to permit it to press upon the horses. 
This limiting slope corresponds to the " angle of repose" 
of mechanical science ; i. e., the angle made with the 
horizon by the steepest plane down which a body will not 
slide of its own accord, its gravity just balancing its fric- 
tion, so that the least increase of slope would overpower 
the resistance of the friction, and make the body descend. 
This " angle of repose" should therefore be the limit of 



GREATEST ALLOWABLE SLOPE. 39 

the slope of a road, for on such an inchnalion a vehicle 
once set in motion would descend with uniform, unaccel- 
erated velocity. This angle varies with the smoothness and 
hardness of the road, and also with the degree of friction 
of the axles of the carriage. On the very best class of 
broken-stone roads, kept in good order, and with a good 
carriage, it is considered by Sir Henry Parnell, from his 
experiments, to be 1 in 35, (or 151 feet to the mile) 
which should therefore be the maximum slope upon the 
best roads.* On such a slope a coach may be driven 
down, with perfect safety and complete control, at the 
speed of twelve miles per hour. 

If the inclination be steeper than this, the danger of the 
descent is greatly increased, and the speed must be less- 
ened. If it be so steep that a carriage cannot be safely 
driven down at a greater speed than four miles per hour, 
on every mile of such a slope there will be a loss of ten 
minutes of time, equivalent to two miles upon a level. 
To avoid such an inclination, a road-maker would 
therefore be justified, by considerations of time-saving, 
in adopting a level route three times as long as the 
steep one. 

When inclinations are reduced to this limit of 1 in 35, 
there is little loss of power, compared with a perfect level, 
in either direction of the travel ; for the increased labor of 
ascending is compensated in a great degree by the in- 
creased ease of descending, while on a steeper slope this 
advantage is nullified by the necessity of the horses holding 
back the carriage to resist the excess of the force of gravity. 

* On such roads Dr. Lardaer considers the angle of repose to be as 
small as 1 in 40 ; while on roads not well freed from mud and dust, tho 
friction increases the angle to 1 in 30 ; and on an inferior class of roads it 
is 1 in 20, or even steeper 



40 WHAT ROADS OUGHT TO BE. 



MAXIMUM SLOPE, CONSIDERED AS AN ASCEMT, 

Suppose that a road is to be carried over a hill, which 
rises 100 feet in a horizpntal distance of 500 feet, {i. e., 
1 in 5) and which cannot be avoided by any horizontal 
circuit within the limits of distance indicated on page 28. 
The question which presents itself is, how steep can the 
slope of a road up the side of this hill be most advanta- 
geously laid out, since, by adopting a zigzag line, the road 
may be made as long and therefore as gentle in the ascent 
as may be desired ? The shortest line would run straight 
up the face of the hill, and this line would give the least 
amount of labor ; but then this labor for horses would be 
impossible : and even if possible, the horses could not 
draw up the whole load which they had been drawing on 
the other parts of the road, nor could they descend it with 
safety. But, on the other hand, the road should approach 
this shortest line as nearly as other considerations will 
permit, since, if it should zigzag excessively for the pur- 
pose of lessening the steepness, it would be so long as to 
increase unnecessarily its cost and the time and labor of 
travel upon it. A medium and compromise between these 
two evils must therefore be found. What shall it be ? 

Supposing the load of a horse on the level portions of 
the road to be as much as he can regularly and constantly 
draw, his power of drawing it up an ascent will depend 
upon how much extra exertion he is capable of putting 
forth. This is not very accurately ascertained or defined, 
and depends very much on the length of the ascent, but 
may be assumed at double his usual exertion.* Now a 
horse drawing a load on a level road of the best character, 

* GayfEer, p. 9. 



GREATEST ALLOWABLE SLOPE. 41 

such as has been previously considered, is obhged by the 
resistance of the friction to exercise against his collar a 
pressure of about one thirty-fiflh of the load. If he can 
just double this exertion, he can lift one thirty-fifth more, 
and the slope which would force him to lift that proportion 
would be (as was shown on page 32) one of 1 in 35. On 
this slope he would therefore be compelled to double his 
ordinary exertion, and on this supposition it would be the 
maximum slope allowable, considered as an ascent. 

These two methods of determining the maximum slope 
(by considering it as an ascent and as a descent) are en- 
tirely independent of each other.* If they give different 
results, the smallest one, or the least slope obtained, must 
be adopted ; for, if it be disadvantageous to employ a 
slope sleeper than 1 in 35, it must a fortiori be still more 
so, to employ one steeper than 1 in 30, or 1 in 20 ; though 
even greater slopes are too often met with. 

Upon most of our American roads the resistance of 
friction would be found to be nearer -^^ than 3'j, and 1 in 
20 would therefore be their maximum slope with their 
present condition of surface. But as it is to be hoped 
that in this respect they will, before long, be greatly im- 
proved, in which case they would demand more and more 
gentle slopes, we should anticipate this desirable consum- 
mation, by giving in advance to all new lines of road at 
least, if not to the faulty old ones, slopes not exceeding 1 
in 30, which seems to be a just medium. 

* They give identical results in this case, only because the extra exer- 
tion happened to be taken as doubled. Suppose it to be tripled. The 
horse can lift ^-^ more, which corresponds to a slope of 1 in 17^. Horses 
can indeed for a short time exercise a tension of six times the usual 
amount, but the above assumption of double is more dependable, though it 
cannot be fixed with the precision which is desirable. 



42 WHAT ROADS OUGHT TO BE. 

The maximum established by L'' administration des Fonts et 
Chaussees, the French government board of engineers of roads 
and bridges, is 1 in 20. This, however, was fixed at a time 
when the usual surface of roads was much inferior to its pres- 
ent condition. 

The great Holyhead road, made by Telford through the 
very mountainous district of North Wales, has 1 in 30 for its 
maximum, except in two cases, (one of 1 in 22, and a very 
short one of 1 in 17) and in them the surface of the road 
was made peculiarly smooth and hard, so that no difficulty is 
felt by loaded vehicles in ascending. On the old line of road, 
the inclinations had been sometimes as great as 1 in 6, 1 in 7, &c . 

On the great Alpine road over the Simplon pass, (which 
rises to a height of a mile and a quarter above the level of 
the sea) the slopes average 1 in 22 on the Italian side, and 1 
in 17 on the Swiss side, and in one case only become as steep 
as 1 in 13. 

In the state of New York several turnpike companies are 
limited by law to a maximum slope of " eighteen inches to a 
rod," i. e. 1 in 11. But this limit ought not to be even ap- 
proached in practice. 

On our " National" or " Cumberland" road the slopes 
in many places are much too great, and its superinten- 
dent, Capt. Wever, writes* that " if the road had been 
very considerably elongated in order to effect a graduation 
at angles not exceeding three degrees, or 1 in 19, (and for 
the maximum, two degrees, or 1 in 29, would be better) 
the road could be travelled in as short a space of time as 
it now is, and the power used could move double the bur- 
den it now can ; thus rendering the road, for commercial 
purposes, doubly advantageous." 

If the ascent be one of great length, it will be advan- 
tageous to make steepest the lowest portion of it, upon 
which the horses come with their full strength, and to 

* Report to United States Chief Engineer, 1828. 



LEAST ALLOWABLE SLOPE. 43 

make the slopes gentler towards the summit of the as- 
cent, to correspond to the continually decreasing strength 
of the fatigued horses. 

MINIMUM SLOPE. 

A true level has been thus far considered to be a most 
desirable attribute, and one to be earnestly sought for, in 
establishing a perfect road. This principle must be qual- 
ified, however, by the announcement that there is a mini- 
mum, or least allowable slope, which the road must not 
fall short of, as well as a maximum one, which it must not 
exceed. If the road were perfectly level in its longitu- 
dinal direction, its surface could not be kept free from 
water without giving it so great a rise in its middle as 
would expose vehicles to the danger of overturning. But 
when a road has a proper slope in the direction of its 
length, not only do the side-ditches readily discharge the 
water which falls into them, but every wheel-track that is 
made, becomes also a channel to carry off the water. 

The minimum slope (flatter than which the road should 
not be) is assumed by an experienced English engineer 
to be one in eighty, or 66 feet to the mile. The minimum 
established in France by the Corps des Ponts* et Chaus- 
sees is .008, or one in a hundred and twenty-five, or 42 
feet to the mile. An angle of one-half a degree is often 
named in this connection ; it equals one in a hundred and 
fifteen. In a perfectly level country the road should be 
artificially formed into gentle undulations approximating 
to the minimum limit. 

Finally, then, lue arrive at this conclusion, that the lon- 
gitudinal slopes of a road should be kept, if possible, be- 
tween 1 in 30 and 1 in 125, never steeper than the former, 
nor nearer to a level than the latter. 



44 



WHAT ROADS OUGHT TO BE. 



TABLES OF INCLINATIONS. 



There being three different methods of specifying de- 
grees of inchnation, (viz. by the angle made with the 
horizon, by the proportion between the ascent and the 
horizontal distance, and by the ascent per mile) it is fre- 
quently desirable to compare the different expressions. 
The following tables show the values which correspond to 
each other. 



Angles. 


Inclinations. 


Feet per mile. 


X° 


1 in 115 


46 




3o 

4 


1 in 76 


69 




1 ° 


1 in 57 


92 




u° 


1 in 38 


138 




2 ° 


1 in 29 


184 




21° 


1 in 23 


231 




3 ° 


1 in 19 


277 




4 ° 


1 in 14 


369 




5 ° 


1 in 11 


462 





Inclinations. 


Angles. 


Feet per mile. 


1 in 10 


5° 43' 


528 


1 in 13 


40 24' 


406 


1 in 15 


3° 49' 


352 


1 in 20 


2° 52' 


264 


1 in 25 


2^ 18' 


211 


1 in 30 


1° 55' 


176 


1 in 35 


1° 38' 


151 


1 in 40 


1° 26' 


132 


1 in 45 


1° 16' 


117 


1 in 50 


1° 9' 


106 


1 in 100 


0° 35' 


53 


1 in 125 


0° 28' 


42 



THEIR CROSS SECTIONS. 45 

3. WHAT ROADS OUGHT TO BE AS TO THEIR CROSS-SECTION. 

The cross-section of a road is the view which it would 
present if cut through at right angles to its length, one of 
the portions being removed. It comprises the following 
subjects of investigation : 

1 . The width of the rocd. 

2. The shape of the road-bed. 

3. Foot-paths, <^c. 

4. Ditches. 

5. The side-slopes of the cuttings and fillings. 

Fiff. 3. 




i^j^sj^^ 



The proper width for a road depends, of course, upon 
its importance, and the amount of travel upon it. Its 
minhnum is about one rod, or 16| feet, sufficient to enable 
two vehicles to pass each other with ease. For ordinary- 
town roads a good width is from 20 to 25 feet. A width 
of 30 feet is fully sufficient for any road, except one which 
forms the approach to a very populous city. 

Any unnecessary width (such as is often adopted in a 
spirit of public ostentation) is injurious, not only from its 
waste of land, but from its increase of the labor and cost of 
keeping the road in repair ; each rod in width adding two 
acres per mile to the area covered by the road. 

In the state of New York, by the revised statutes, "All 
public roads, to be laid out by the commissioners of high- 
ways of any town, shall not be less- than three rods wide." 

This is to be the width between fences ; and no more 



46 WHAT ROADS OUGHT TO BE. 

of it need be worked, or formed into a surface for travel 
ling upon, than is deemed necessary. 

The same laws declare, " It shall be the duly of the 
commissioners of highways to order the overseers of high- 
ways to open all roads to the width of two rods at least, 
which they shall judge to have been used as public high- 
ways for twenty years." 

It is also ordered that '"' all private roads shall not be 
more than three rods wide." 

Turnpike-roads are obliged by the statute to be " laid 
out not less than fou7~ rods wide," and " twenty-two feet 
of such width to be bedded with stone," &c. When a 
precipitous locality renders the full width impracticable, 
" tioenty-two feef is the minimum width permitted. 

■ Where a road ascends a steep hill-side by zigzags, 
it should be wider on the curves connecting the straight 
portions. The width of the roadway may be increased 
about one-fourth, when the angle between the straight 
portions of the zigzags is from 120° to 90° ; and the in- 
crease should be nearly one-half, when the angle is from 
90° to 60°.* 

The Roman military roads had their width established, by 
the laws of the Twelve Tables, at twelve feet when straight, 
and sixteen when crooked ; barely sufficient for the army, bag- 
gage, and military machines. 

The French engineers make four different classes of roads.") 
The first class comprises such as pass from the capital of 
one country to that of another. Their width is GG feet, of 
which 22 in the middle are stoned or paved. 

Those of the second class pass from the metropolis of a 
country to its other great cities. Their width is 52 feet, of 
which 20 in the middle are stoned. 

Those of the third class connect large towns with each other 



» Mahan, p. 282. t Gayffier, p. 90 



THEIR WIDTH. 47 

and with first-class roads. Their width is 33 feet, with 16 
feet in the middle stoned. 

The fourth class contains common town roads. Their width 
is 26 feet, with the same middle causeway as the last. 

In England, the prescribed width for turnpike-roads at the 
approach to populous towns is 60 feet. The limits of by-roads 
are, for carriage-roads, 20 feet ; for horse-roads, 8 feet ; and 
for foot-paths, 6| feet.* 

Tslford's Holyhead road, a model road for a hilly country, 
has the following width in the clear within the fences : 32 feet 
on flat ground ; 28 feet when there are side-cuttings less than 
three feet deep ; and 22 feet along steep ground and precipices. 

The United Slates National or Cumberland road has 80 
feet in width cleared, but the road itself is only 30 feet. 

The broken-stone road between Albany and Troy is 32 feet 
wide, besides two sidewalks of 8 feet each. 

The " Third Avenue" of the city of New York is 60 feet 
wide between the sidewalks, each of which occupies 20 feet : 
26 feet of its middle are stoned. 

Broadway, New York, is 80 feet wide between the houses, 
of which 19 feet on each side are occupied by the foot-pave- 
ments, leaving 42 feet for the carriage-way. 

When broken-stone roads are adopted, it is usual, for 
the sake of a saving in the first cost, to make only a cer- 
tain width or " causeway," in the middle of the road, of 
the harder material, and to form the sides, or " wings," of 
the natural earth, (or of broken stone, if the causeway be 
a pavement) which will be preferable in summer and for 
Ught vehicles and horsemen. f Sixteen feet for the mid- 
dle and twelve for the sides is a common proportion. 

If the stoned part be made narrower than just wide enough 
for two carriages to pass upon it, it should be made only wide" 

* Roads and Railroads, p. 73. 

t A serious objection to this plan is, that the wheels which cross the 
road, and are alternately on the stone and on the earth, will deposite earth 
upon the stone surface, to the great deterioration of its advantages. 



48 WHAT ROADS OUGHT TO BE. 

enough for one ; for any intermediate width will be a waste of 
all the surplus beyond what one requires. 

If the road is to be made wider than two vehicles require, 
(which strictly is only 12 feet) it should be enlarged at once to 
23 feet ; for any intermediate width will cause unequal and ex- 
cessive wear, and therefore be false economy : an unexpected 
conclusion, which results from an investigation of Gayffier, 
pages 184-8. 

It would be preferable to place the harder material on 
the sides of the road, instead of on the centre ; for the 
drivers of heavily-laden vehicles will generally keep them 
on the sides of the road, so that they can walk on the foot- 
paths ; and if this part be not of the hardest material, it 
will soon be cut up and rutted by the heavy wagons fol 
lowing each other in the same track.* 

SHAPE OF THE ROAD-BED. 

In forming the road-bed, or travelled part of the road, 
the first and most important point, in a flat country, is to 
raise it above the level of the land through which it passes, 
so that it may be always perfectly free from water ; a 
precaution which is one of the most essential requisites 
for keeping a road in good condition. Roads are often 
placed in a hollow-way, (or even a trench is dug, when 
better materials are to be added) and their surface is 
allowed to remain so low, that they form excellent gutters 
to drain the adjacent fields, at the expense of t|ie comfort, 
labor, and time of all who travel them. Even the best 
_ ditches cannot always secure them from the land-springs, 
(which will sometimes pass under the ditches by fissures 
which form inverted siphons) and the only effectual means 
will be the raising of the surface by an embankment of 

* Parnell, p. 129 



THEIR SHAPE, 49 

two or three feet. The excavations for the ditches should 
invariably be thus applied. 

The necessary elevation having been established, the 
shape of the road-bed, at right-angles to its length, or its 
"transverse profile," must be decided upon. 

The road must not be flat, but must " crov^n," or be 
higher in its middle than at its sides, so as to permit the 
vi^ater of rains to rapidly run off into the side ditches. If 
originally flat, it is soon worn concave, and its middle 
becomes a pool, if it be on level ground ; or a water- 
course, if it be on an inclination. In the former case, the 
road becomes mud ; in the latter, the smaller materials 
are washed away, and the larger stones left bare. Both 
these evils are of continual occurrence on our country 
roads, but may be easily prevented, by shaping the road 
according to the instructions to be presently given. 

The usual, though improper, shape given to a road in 
order to make it crown, has been a convex curve, ap- 
proaching a segment of a circle, or a flat semi-ellipse. 

Fig. 4. 

^- ^^ 




Though recommended by high authorities, it is very 
faulty, in consequence of its slope not being uniform, 
(the proportion between arcs and versed sines constantly 
changing) and giving too little inclination near the middle, 
and too much at the sides. From this peculiarity the 
following evils result : — 

1. The water stands on the middle of the road, and 
washes away its sides. 

2. It is worn down very unequally : for all carriages, to 
avoid the danger of overturning on the steep sides, will 

4 



50 WHAT ROADS OUGHT TO BE. 

take the middle of the road, which is the only part of it 
where they can stand at all upright ; while the road ought, 
on the contrary, to be so formed as to induce vehicles to 
traverse it equally and indifferently in every part. 

.3. This excessive travel on the middle soon wears it 
into ruts and holes, so that more water will actually stand 
upon such an originally convex road than on one reason- 
ably flat. 

4. When carriages are forced to travel on the sides, 
they cause great additional wear to the road, from their 
constant tendency to slide down the sides, owing to the 
oblique angle at which the direction of gravity meets the 
surface. 

5. As this sliding tendency is at right-angles to the line 
of draught, the labor of the horses and the wear of the 
wheels are both greatly increased. 

6. Whenever vehicles are obliged to cross the road, 
and mount the central ridge, they must overcome the 
same resistance of gravity, as when they are drawn up a 
longitudinal hill. 

The best transverse profile for a road on level ground, 
is that formed by two inchned planes, meeting in ihn 

Fiff. 5. 



centre of the road, and having their angle slightly rounded 
by a connecting curve. The inclinations thus formed will 
be uniform, and the road will thus escape most of the 
evils incident to the curved profile. 

The degree of inclination of theSe planes will depend 
on the surface of the road ; being greatest where the road 
is rough, and lessening with its improvement in smooth 



THEIR SHArE. 51 

ness. It may also be somewhat less on a narrow road, 
as the water will have a less distance to pass over. Its 
maximum is limited by the inconvenience which an ex- 
cessive transverse slope would cause to carriages. A 
proper medium for a road with a broken-stone surface, is 
1 in 24, or half an inch to a foot. Telford, in his Holy 
head road, adopted 1 in 30, or 6 inches crown in a road 
of 30 feet ; and McAdam 1 in 36, and even 1 in 60, or 3 
inches in a 30 feet road. On a rough road the inclination 
may be increased to 1 in 20 ; and diminished on a road 
paved with square blocks to 1 in 40, or 1 in 50. 

Up to these limits the transverse slope should increase 
with the longitudinal slope of the road, which it should 
always exceed, in order to prevent the water running 
too far down the length of the road, and gullying it out ; 
for the water of rains runs off from the middle of a road 
in the diagonal of a rectangle, the sides of which are pro- 
portioned to the steepness of the two slopes, longitudinal 
and transverse. 

If these slopes be equal, the rectangle becomes a square, 
and the direction of the escaping waters makes an angle of 
45° with the direction of the road. pj„ g_ 

If the transverse slope be double the 



longitudinal, the waters in their di- I / 

«i / 
agonal course make an angle of 63^0 \/ 

with the road, as in the figure. If |\ 

the road be level longitudinally, they \ \ 

run off at right angles. 



-^~ 



On a steep side-hill, the transverse profile should be a 
single slope, inclining inwards from the outer edges of the 
road to the face of the hill. The ditch should be on the 
side of the hill, and its waters be carried at proper inter- 
vals under the road to its outside. This form is particu- 



52 



WHAT ROADS OUGHT TO BE. 
Fiff. 7. 




larly advantageous when the road curves rapidly around 
the hill, since it counteracts the dangerous centrifugal 
force of the vehicles. It may, therefore, be also adopted 
on the curves of a road in embankment. 

Through villages, where space must be economized, 
and the side ditches dispensed with, the middle portion 

Fig. 8. 



of the road is made to descend each way from the centre 
as usual, but the sides slope upwards towards the houses. 
Two farrovi^s, or shallow water-channels, are thus formed, 
which should be paved to a width of two feet on each 
side of their middle. This form may also be used on a 
hill-side. 

A frequent, but very bad shape, is hollow in its middle, 
in which the waters run. Its faults are, that carriages 
slide down towards each Fig. 9. 

other, especially in frosty 
weather, and that the 
large stream in the mid- 
dle washes away the road. It should never be used ex- 
cept when the width is greatly contracted, and when it is 
absolutely impossible to obtain room for ditches. 




FOOTPATHS AND DITCHES. 53 

FOOTPATHS, &C. 

On each side of the carriage-way should be flat mounds, 
raised six inches above the road. Sods, eight inches wide 
and six inches thick, should be laid against these mounds in 
such a manner as to form a sloping edge. The water which 
falls on the surface of the road runs along the bottoms of 
these sods, in the " side channels" formed by them, till it 
passes off under the mounds into the ditches. These 
mounds, in a great road of thirty feet width, should be six 
feet wide, and their surfaces should be inclined 1 inch in 
a yard. One of them should be covered with gravel for 
a footpath, and the other be sown with grass-seed. Their 
general adoption would greatly increase the safety of night- 
travelling, the accidents in which often occur from running 
on high banks or into ditches. They are not high enough 
to overturn a coach when one wheel runs upon them, but 
they indicate at once that the carriage is leaving the road. 

Outside of the footpaths should be fences, (or hedges, 
where the climate will permit) and outside of the fences 
should be the ditches. These mounds, ditches, &c., are 
shown in Fig. 3. 

DITCHES. 

The drainage of a road by suitable ditches is one of the 
most important elements in its condition. All attempts at 
improvement are useless till the water is thoroughly got 
rid of, and a bad road may often be transformed into a 
good one, by merely forming beside it deep ditches, suffi- 
ciently inclined to carry off immediately all the water 
which falls upon it. Even if the water does not stand on 
the surface so as to form mud, if it filtrates from the 
higher land beside it, and from springs under it, and is not 



54 WHAT ROADS OUGHT TO BE. 

well drained off, it will weaken the substratum of the road 
SO as to render it incapable of bearing heavy loads, and 
will be absorbed into the upper stratum by capillary attrac- 
tion. If the road have a covering of broken stones, the 
water penetrating into it makes them wear away very rap 
idly by assisting the vibrating motion of their fragments, 
as lapidaries grind down the hardest stones by their own 
dust, with the aid of water. 

The ditches should lead to the natural water-courses of 
the country; and should, if possible, have a minimum slope 
of one in a hundred and twenty-five, corresponding with 
the " minimum slope" of the road, though less will suffice 
if the bottom be truly cut and kept free from grass. They 
should generally be sunk to a depth of three feet below 
the surface of the road. Their size will be regulated by 
their situation, being greater where they intercept the wa- 
ter from side-hills rising above the road, and also where 
the country is humid, A width of one foot at bottom, 
with side-slopes depending on the nature of the soil, will 
generally suffice. In wet soils the ditches should be so 
wide and deep, that the earth taken from them may be 
sufficient to raise the bed of the road between them three 
feet higher than the natural surface. 

There should be a ditch on each side of the road on 
level ground, or in cuttings, and on the upper side of the 
road, where it is on a hill-side. The water from the side 
channels must be carried into these, and the contents of 
the ditches must pass under the road to the natural water- 
courses by means of drains, culverts, &c., as will be ex- 
plained in Chapter III. under the head of " Mechanical 
Structures." 



SIDE-SLOPES. 55 



SIDE-SLOPES OF THE CUTTINGS AND FILLINGS. 

These are designated by the proportion between the 
base and perpendicular of the right-angled triangle, of 

Fig. 10. 




90 



which the slope is the hypothenuse, the base being al- 
ways named first, and the perpendicular being the unit 
of measure. Thus, if a cutting of ten feet in depth 
goes out twenty feet, as in the figure, its slope is said 
to be 2 to 1 ; if it goes out but five feet, it is said to be 
|tol. 

The Slopes of Cuttings or Excavations vary with the 
nature of the soil, being made for economy as steep as 
its tenacity will permit. Solid rock may be cut vertically, 
or at a slope of i to 1. Common earth will stand at 1 to 
1, or at 11 to 1 ; the latter is safer. Gravel requires 1|- 
to 1. Some clays will stand at 1 to 1 ; while some, 
originally sloped 2 to 1, have slipped till they have as- 
sumed a slope of 6 to 1 . The proper degree of slope is 
best determined by observing that at which the earth in 
question naturally stands. Heavy clayey earth will as- 
sume a slope of I to 1, and very fine dry sand of nearly 
3 to 1 ; these are the extremes in ordinary cases. 

Deep cuttings should not, however, be made with less 
slopes than 2 to 1, (even thdugh they would stand steeper) 
so that the sun and wind may freely reach the road to 
keep it dry. The south side of excavations may be made 



56 



WHAT ROADS OUGHT TO BE, 



Fig. 11. 



even 3 to 1, when the extra earth can be profitably used 
in a neighboring embankment. 

When the lower part of a cutting is in rock, and has a 
steep slope, and 
the upper portion 
in earth has a 
much flatter one, 
a wide " bench," 
or offset, should 
be made, where 
the change of ^^ 
slope takes place. 

The following Table shows the angle with the horizon 
made by slopes of various proportions of base to height. 




Slopes. 


Angles. 


i to 1 


75° 58' 


i to 1 


63° 28' 


1 to 1 


53° 8' 


1 to 1 


45° 


U to 1 


38° 40' 


li to 1 


33° 42' 


1^ to i 


29° 44' 


2 to 1 


26° 34' 


3 to 1 


18° 26' 


4 to 1 


14° 2' 


5 to 1 


11° 19' 


6 to 1 


9° 27' 



Fillings or Embankments have less variety than cuttings 
in the nature and condition of their materials, and there- 
fore have less variety of slope, which is usually 1| to 1, 
or 2 to 1 ; though some clays (which should, however, 
never be employed, if their use can be avoided) require 
3 or 4 to 1, when more than four feet high. 



SIDE-SLOPES. 57 



CURVED SIDE-SLOPES. 

The customary form of the side-slopes of cuttings and 
fiUings — that of an inchned plane — is not the form of 
most perfect equilibrium and stability. To secure this, 
the slope may be steep near its top, with its upper angle 
rounded off, but must widen out at its bottom, where the 
pressure is the greatest. This is the natural face which 
an excav3,tion assumes when left to itself, as shown in 

Fig. 12. 



the figure. Its top, or salient angle, becomes convex ; 
and its bottom, or re-entering angle, is filled up into a 
concavity, thus forming a curve of contrary flexure. If 
side-slopes were originally formed into this shape, they 
would be much more permanent, and the elements, rain, 
gravity, &c., would then work with man, and assist the 
labors of art, instead of destroying them, as when the 
usual form is employed. This curve of stability is more- 
over that of beauty, coinciding with Hogarth's " line of 
grace." 

This plan is not known to have been ever put into 
practice, though the walls supporting a bank, particularly 
for a quay, are sometimes made concave outwardly ; and 
the dam of the Croton Aqueduct has, for its outer profile, 
somewhat such a curve as has been above recommended. 



58 WHAT ROADS OUGHT TO BE. 



4. WHAT ROADS OUGHT TO BE AS TO THEIR SURFACE. 

QUALITIES DESIRABLE. 

The surface of a road ought to be as smooth and as 
HARD as possible, so as to reduce to their smallest possible 
degree the resistances oi elasticity, collision, and friction. 

Smoothness is not only essential to comfort, but even 
more so to economy of labor, of carriage-wear, and of road 
wear. Carriages passing over a smooth road are not only 
drawn more pleasantly, and with less exertion of animal 
strength, but also do much less damage to the road, than 
when it has hollows into which the wheels fall with the 
momentum of sledge-hammers, each blow deepening the 
hole and thus increasing the force of the next blow. 

Hardness is that property of a surface by which it re- 
sists the impression of other bodies which impinge upon 
it. It is essential to the preservation of smoothness, ex- 
cept in the case of elastic surfaces. 

RESISTANCES TO BE LESSENED. 

Elasticity. — A road may be perfectly smooth, both be- 
fore and after a vehicle has passed over it, but if it sink 
in the least under the passage of a wheel, this yieldii/g 
presents before the wheel a miniature hill, up which the 
vehicle must be raised with all the loss of power demon- 
strated on page 32. If the depression were one inch, and 
the wheel four feet in diameter, an inclined plane of 1 in 
7 would be formed, and one-seventh of the entire weight 
would need to be lifted up this inch. A road surface of 
caoutchouc, or India-rubber, of the snost perfect smooth- 
ness, would therefore be the worst possible for traction, 
though very pleasant for passengers. The wheels would 



RESISTANCES TO BE LESSENED. 



59 



always be in depressions, and the horses would be always 
pulling up hill. An elastic bottom for a road, such as 
a boggy substratum, would for this reason cause great 
waste of draught. A solid, unyielding foundation is 
therefore one of the first requisites for a perfect road. 

Collision. — The resistance of collision is occasioned 
by the hard protuberances, inequalities, stones, and other 
loose materials of a road against which the wheels strike, 
with great loss of momentum and waste of the power of 
draught ; for the carriage must be lifted over them by the 
leverage of the wheels. It is, therefore, most important 
that such obstacles should be as few and as small as pos- 
sible, the resistance being proportional to their size, as 
appears in the investigation which follows. 



The power required to draw a wheel over a stone or any obsta- 
cle, such as S in the figure, may be thus calculated. Let P repre- 
sent the power sought. 



Fig. 13. 



or that which would 
just balance the weight 
on the point of the 
stone, and the slightest 
increase of which would 
draw it over. This 
power acts in the di- 
rection CP with the 
leverage of EC or DE. 



Gravity, represented by 

"W, resists in the direction CB with the leverage of BD. The 

equation of equilibrium will be P X CB = W X BD, whence 

VCD' — BC= 
P — 




BD 



CD — AB • 

Let the radius of the wheel =: CD =: 26 inches, and the 
height of the obstacle := AB = 4 inches. Let the weight W 
= 500 lbs., of which 200 lbs. may be the weight of the wheel, 
and 300 lbs. the load on the axle. The formula then becomes 



60 WHAT ROADS OUGHT TO BE. 

^676 — 484 13.85 

P =: 500 — _ = 500 — — = 314.3 lbs. The pres- 
sure at the point D is compounded of the weight and the 

power, and equals W — — = 500 X — =:5911bs.,andtherefore 
^ ' ^ CB 22 ' 

acts with this great effect to destroy the road in its collision 

with the stone, in addition to its force in descending from it. 

For minute accuracy, the non-horizontal direction of the 

draught, and the thickness of the axle, should be taken into 

the account. 

The power required is lessened by proper springs to vehi- 
cles, by enlarged wheels, and by making the line of draught 
ascending. 

The resistance produced by the hollows between the stones 
of a pavement is of a different nature. According to the in- 
vestigations of M. Gerstner, the resistance arising from such 
a surface is directly proportional to the load, to the square of 
the velocity, and to the ratio of the width of the cavity to the 
radius of the wheel ; and inversely proportional to the width 
of the paving stones. 

Friction. — The resistance of friction arises from the 
rubbing of the wheels against the surfaces with which 
they come in contact, and will always exist, however the 
surface may be improved. Its two extremes may be 
seen on a road of loose gravel, and on a railroad. It is 
greatly increased when the surface is covered with mud, 
or other loose material, into which the wheel may sink, 
and thus give a wider contact. The degree in which 
it is influenced by the surface, may be shown by rolling 
an ivory ball successively over a carpet, a fine cloth, a 
smooth floor, and a sheet of ice ; the distances to which 
the same force will impel it over these surfaces increasing 
in the order in which they have been named. 

The surface of a road may be improved by the various 
methods of diminishing the friction, to be examined in 



FRICTION. 61 

Chapter IV., such as " Macadamizing" the road, or cov- 
ering it with a layer of finely broken stones ; paving with 
smooth stone blocks ; covering with planks ; or laying 
wheel-tracks of stone, wood, or iron. 

The friction on all these surfaces is different, and can 
be determined only by experiment. The instrument used 
for measuring it is called a Dynamometer. It resembles 
in principle and general construction the " spring-balan 
ces" in common use, in which the application of a weight 
compresses a spiral spring, the shortening of which, as 
shown by a properly graduated scale, indicates the 
amount of weight applied. In the dynamometer the 
power takes the place of the weight of the spring-balan 
ces, one end of the instrument being connected with the 
carriage, and the other with the horses, and the force 
which they exert to overcome the friction being shown by 
the index. 

Sir John Macneill has greatly improved the instrument, by 
adapting to it a piston working in a cylinder full of oil, which 
lessens the vibrations of the index, and enables its indications 
to be read with more ease and precision. He has also added 
to it a contrivance for making the instrument itself record the 
degree offeree exerted at each moment of motion. It likewise 
registers the distance passed over, and the rises and falls of 
the road.* 

This valuable instrument affords a means of ascertaining 
the exact power required to draw a carriage over any line of 
road ; it will thus enable one line of road to be compared with 
another, and their precise amount of difference in ease of 
draught, to be determined ; it will show the comparative value 
of the different methods of improving the surface; and it will 
enable a registry to be kept from year to year of the state of a 
road, showing where and how much it has improved or de- 

* For a full description of this instrument, see Parnell, pp. 327-347. 



65 

Ad 


= 


1 
1 




— 


51 


33 


= 


1 
IT 


121 


z=z 


1 

1 79 


8 


= 


2h 



62 WHAT ROADS OUGHT TO BE. 

teriorated, and therefore how judiciously, or the contrary, the 
funds expended on it have been applied. 

The following are the results of experiments made with this 
instrument on various kinds of road. The wagon employed 
weighed 21 cwt., and the resistance to draught was as fol- 
lows : — 

* On a gravel road, laid on earth — per 21 cwt., 1471bs.= Jg- 

* On a broken-stone road, " " 

* " on a paved"foundation, " 

* On a well-made pavement, " 
f On the best stone track- ways, per gross ton, 
J On the best form of railroad, " 

From the above experiments we infer, in round num- 
bers, taking the maximum load on a gravel road for the 
standard, that a horse can draw — 

On the best broken-stone road, 3 times as much. 
On a well-made pavement, 4|- times as much. 

On the best stone track-ways, 1 1 times as much, 
On the best railways, 18 times as much. 

Poncelet^ gives the following relations of the friction to 

the pressure, for wheels with iron tires rolling on different 

surfaces : — 

On a road of sand and gravel, ^ 

rv 1 1 , 1 i in ordinary condition, Jr 

On a broken-stone road, < • ^ ^^ ,.,. ' V 

( m periect condition, -^ 

On a pavement in good order, j + t t ' 2 

On oak planks not dressed, ' -^-^ 

The most complete series of experiments upon the friction 
of vehicles have been recently made by M. Morin.\ Some of 
the most important results are given below, in a tabular form. 
The fractions express the relation of the force of draught to 
the total load, vehicles included. 

* Parnell, pp. 43, 73. t Ibid. p. 107. 

X Lecount, p. 219. § M6canique Industrielle, p. 507. 

11 Aide-M^moire de Mecaiiique, p. 337. 



FRICTION. 



63 



CHARACTER OF 
THE ROAD. 


CHARACTER OF THE VEHICLE. | 


Carls. 


Trucks 
(of 2i 
loiis.) 


Diligences 
(of five tons.) 


Carriug-es 

with seals hung 

on springs. 


New road, covered 
with gravel five 
inches thick, 


tV 


1 

9 


1 
3 


1 
8 


Solid causeway of 
earth, covered with 
gravel 1|- in. thick. 


1 

1 e 


1 
1 1 


1 


1 
1 


Causeway of earth 
in, very good con- 
dition. 


4 1 


1 
2 9 


1 

26 


1 

26 


Oaken platform. 


1 
1 


1 

40 


1 
4T 


1 
4 2 


Broken-stone road. 

Very dry and smooth. 
Moist or dusty. 
With ruts and mud. 
Deep ruts and thick ) 
mud, \ 


_U 

S 3 

1 
3 3 

1 
1 9 


1 
5 4 
Jl_ 
3 8 

1 
2 4 

1 
1 4 


V/alk. 


Trot. 


Walk. 


Trot. 


4 8 

1 
34 

1 
2 1 

1 
1 2 


1 
4 1 

1 
27 

I 
1 3 

1 
1 


1 

4 9 

1 
34 
_1_ 

1 
I 2 


1 

4 2 
1 

2 7 
1 
19 

tV 


Pavement, \ ^^^j . ^ 
^ muddy, j -g\ 


1 
6 S 

1 
5 


5V 

1 
4 4 


J- 
3 8 

1 
3 3 


45 


I 

39 

1 
34 



From the above table it is apparent how important is 
the condition in which the best-made road is kept, and 
how gi-eatly the labor of draught is increased by mud or 
dust on its surface. The character of the vehicle is also 
seen to have great influence on the degree of friction. 

The principal general results, deduced by M. Morin 
from the elaborate experiments above referred to, are 
given on the following page. 



64 WHAT ROADS OUGHT TO BE. 



DEDUCTIONS FROM MORIN S EXPERIMENTS. 

1. The resistance, or " Traction," is directly propor- 
tional to the load, and inversely proportional to the diam- 
eter of the wheel. 

2. Upon a paved, or a hard Macadamized road, the re- 
sistance is independent of the width of the tire when it 
exceeds from 3 to 4 inches. On compressible roads, the 
resistance diminishes when the breadth of the tire in- 
creases. 

3. At a walking pace, the traction is the same, under 
the same circumstances, for carriages with springs, or 
without them. 

4. Upon hard Macadamized and upon paved roads, the 
traction increases with the velocity; the increments of 
traction being directly proportional to the increments of 
the velocity, above a speed of about 2i miles per hour ; 
but it is less as the road is more smooth, and the carriage 
less rigid, or better hung. 

5. Upon soft roads of earth, or sand, or turf, or roads 
freshly and thickly gravelled, the traction is independent 
of the velocity. 

6. Upon a well-made and compact pavement of hewn 
stones, the traction at a walking pace is not more than 
three-fourths of that upon the best Macadamized road 
under similar circumstances : at a trotting pace it is equal 
to it. 

7. The destruction of the road is in all cases greater as 
the diameters of the wheels are less ; and it is greater in 
carriages without than with springs. 



COST AND REVENUE COMPARED. 65 



5. WHAT ROADS OITGHT TO BE AS TO THEIR COST. 

A minimum of expense is, of course, highly desirable ; 
but the road which is truly cheapest is not the one which 
has cost the least money, but the one which makes the 
most profitable returns in proportion to the amount which 
has been expended upon it. 

To lessen the cost of the construction of a road, while 
striving to attain the attributes which we have found to be 
desirable, we should endeavor to avoid the necessity of 
making high embankments, or deep excavations, or any 
rock-cuttings; the cuttings through the hills should just suf- 
fice to fill up the valleys crossed ; the line of the road should 
be carried over firm ground and such as will form a good 
surface if no artificial covering be used ; or if it is to be 
Macadamized, it should pass near some locality of good 
stone ; and it should be so located as to require but few 
and small mechanical structures, such as bridges, culverts, 
retaining walls, &;c. 

COMPARISON OF COST AND REVENUE. 

The more nearly, however, the road is made to ap- 
proximate towards " what it ought to be," the more diffi- 
cult will it be to satisfy the demands of economy. Some 
medium between these extremes must therefore be adopt- 
ed, and the choice of it must be determined by the amount 
and character of the traffic on the road which it is pro- 
posed to make or to improve. For this purpose an accu- 
rate estimate is to be made of the cost of the proposed 
improvement, and also of the annual saving of labor in 
the carriage of goods and passengers which its adoption 
will produce. If the latter exceed the interest of the for- 

5 



66 WHAT ROADS OUGHT TO BE. 

mer, (at whatever per centage money for the investment 
can be obtamed) then the proposed road will be " what 
it ought to he as to its cost" From these considerations 
it will appear that it may be truly cheaper to expend ten 
thousand dollars per mile upon a road which is an impor- 
tant thoroughfare, than one thousand upon another road in 
a different locality. 

" How to estimate the cost ot a road" will be considered 
at the end of Chapter II., which treats of its " Location." 
Under the present head, we will examine how we may 
estimate the probable profits of a road, and from the com- 
parison of the two estimates determine how much the 
projectors of an improved road would be justified in ex 
pending upon it. 

AMOUNT OF TRAFFIC. 

Let us suppose that it is proposed to improve a road in 
any way, whether by Macadamizing its surface, by short- 
ening it, or by carrying it around a hill which it now goes 
over. The first point to be ascertained is the quantity 
and nature of the traffic which already passes over the 
line. This may be most accurately found by stationing 
men to count and note down all that passes in a given 
time of average activity ; and from a sufficient number of 
such returns, well classified, deducing the annual amount. 

COST OF ITS TRANSPORTATION. 

The cost of conveying this amount of traffic is next to 
be calculated. To simplify the question, we will neglect 
the gain in speed, and consider only the saving in heavy 
transportation. Assume that over the road, thirty miles 
in length, 50,000 tons of freight are annually carried, and 
that the average friction of its surface (as determined by 
a dynamometer) is --^ of the weight. The annual force of 



PROFITS OF IMPROVEMENTS. 67 

draught required is therefore 2500 tons, or 5,000,000 lbs. 
If the average power of draught of a horse at 3 miles an 
hour for 10 hours a day be taken at 100 lbs.,* there would 

be required ~ — ~ — = 50,000 horses working at 3 miles 

per hour. At this rate they would traverse the road in 
10 hours, or a working day, and the total amount of labor 
would equal 50,000 days' work of a horse, or $37,500, 
taking 75 cents for the value of one day's work. 

PROFIT OF IMPROVING THE SURFACE. 

Suppose now that the road is to be macadamized, or 
planked, or in any way to have the friction of its surface 
reduced to -^\. The total force of draught will then be 

50,000 X 2000 ^ 2 QQQ QQQ j{jg_ ^ 20,000 horse power, at 
50 f ^ 

3 miles per hour, for 30 miles, or 10 hours = 20,000 days' 

work of a horse. This is a saving from the former amount 

of 30,000. Taking the value of the day's work of a horse 

at 75 cents, i22,500 would be the actual saving of labor 

in each year, by the improvement proposed, which amount 

the carriers could afford to pay, (either in tolls, or in raa- 

* The power of a horse at different velocities is very variable, and, in 
spite of many experiments, is not yet ascertained with the precision de- 
sirable. The usual conventional assumption is 150 lbs. moved 20 miles a 
day at the rate of 2^ miles per hour. This is equivalent to Watts' horse- 
power of 33,000 lbs. raised 1 foot in 1 minute. Tredgold's experiments 
give 125 lbs. moved 20 miles a day at 2^ miles per hour. Sraeaton gives 
100 lbs. moved at same rate ; and Hachettc 128 lbs. Numerous careful 
experiments on an English railway (detailed in " Laws of Excavation 
and Embankment on Railways," page 105) give 110 lbs. moved 19.2 
miles per day at the rate of 2.4 miles per hour. Gayffier (page 178) fixes 
the power for a strong draught-horse at 143 lbs. for 22 miles per day at 
2| miles per hour ; and for an ordinary horse, at 121 lbs. for 25 miles per 
day at 2 J miles per hour. As the speed of a horse increases, his power of 
draught diminishes very rapidly, till at last he cau only move his own weight 



68 WHAT ROADS OUGHT TO BE. 

king the improvement themselves) for their diminished 
expenditure on horses. If money were borrowed at 6 per 
cent., $375,000 would be the amount which could be 
expended in making the improvement, supposing the data 
to have been correctly assumed. If the improvement can 
be made for any amount less than this, the difference will 
be so much clear gain. 

PROFIT OF LESSENING THE LENGTH. 

Next, suppose that the improvement is only shortening 
the road a mile, by a new location of part of it. One- 
thirtieth of the original distance, and therefore labor, is 

saved, or — ^tt"— 1667 days' work of a horse =$1,250 

= interest of $20,833. Add to this the amount which the 
construction of this extra mile would have cost, and if the 
proposed improvement can be made for the sum of the 
two, or even a little more, it should be at once carried into 
effect ; for, besides the saving in the original cost and in 
the annual labor, there is also that of time, and of the for- 
mer cost of repairs of the extra mile, which is now dis- 
pensed with. 

PROFIT OF AVOIDING A HILL. 

If the improvement be avoiding a hill, the resistance 
of gravity is to be compared with that of friction. Sup- 
pose that a certain road ascends a hill which is a mile 
long, and has an inclination of 1 in 10, and descends the 
other side \vhich has the same slope, and that a level route 
can be obtained by making the road a mile longer. It is 
demanded how much may be expended for this purpose. 
Suppose that the friction on this road is ^-^, and that 
50,000 tons, as before, pass over it annually. On the 
original road of two miles, the force of draught required 



PROFITS OF IMPROVEMENTS. 69 

^ . . . 50,000 X 2000 
to overcome friction is — -rz — — — = 25,000 horse 

-' 40 X 100 

. ■^ 1 25,000 X 2 
power, at 3 miles per hour, or = 16,667 hours 

for the 2 miles = 1 667 days' work of a horse. To over- 
come the gravity of the loads on the inclination of 1 in 10 

. 50,000 X 2000 ^ „ „ ^ 

requires—^ — -=10,000,000 lbs. for 1 mile = 

333,3,33 lbs. for 30 miles = 3333 days' work of a horse. 

The descent of a mile on the other side of the hill is not 

a compensation, for a horse will have no more to take 

down the descent than he had dragged up the ascent. 

The total annual labor to overcome both friction and 

gravity on these two miles is therefore 1667 + 3333=5000 

days' work of a horse. 

Upon the new road proposed, there is no inclination to 

overcome, but an extra mile of length. The force of 

r • • • 50,000x2000 ^^ ^^ 

draught upon it due to iriction is — = 2,500,000 

lbs. for 3 miles = 250,000 lbs. for 30 miles = 2500 days' 
work of a horse. The saving of labor is therefore 
5000 — 2500 = 2500 days' work of a horse = $ 1 875 = in- 
terest of $31,250, which amount (deducting cost of repairs 
of the extra mile) may be expended in making the new road. 
These calculations have been made for extreme cases, 
in order to make the principle more striking, but the ad- 
vantages deduced from them have fallen short of the truth, 
since only the original amount of traffic has been consid- 
ered, while all experience shows that this is very greatly 
increased by any improvement in the means of transport, 
particularly by the increased speed, which is an inciden- 
tal advantage w^hich we have not taken into account. 
This increase of traffic cannot, however, be determined 



70 WHAT ROADS OUGHT TO BE. 

in advance, by mathematical calculation, though we can 
readily see from how wide a belt of country the inhabit- 
ants might profitably avail themselves of the improved 
road, and will do so eventually ; but how many of 
them will at once profit by it depends on considerations 
of taste, feeling, and prejudices, which are beyond the 
power of numbers. 

CONSEQUENT INCREASE OF TRAVEL. 

To ascertain from what distances to the right or left on 
either margin, the improved road might expect to attract 
travel to itself from other thoroughfares by the cross- 
roads, the lollowing course of reasoning may be employed. 
Let AB be a portion of the improved 
road, connecting the points A and B. 
Let C be a town connected with the 
other two points by the old unimproved 
roads CA and PB. It is required to de- 
termine w^hether the travel from C to A 
can with the least cost (the cost being 
compounded of time and labor) go to A 
by the old road CA, or take the old cross- 
road CB to the nearest point B of the 
improved road, and then follow the latter 
to A. 

The first point is to ascertain the ratio of improvement of 
the new road compared with the old, or its ratio of diminution 
of cost of travel. For simplicity of calculation let us call 
this ratio two. Denote the miles in AC by m, in AB by n, and 
in BC by x. The relative cost of travel over the line AC will 

n 
also be m, over BC it will be x, but over AB it will be only -. 

If. then, X -{ < m, it will cost less to make the circuit 

from C to A through B ; and both routes will be equal in cost 
■when a; -{- — = m. In this calculation, therefore, the hypothe- 
nuse equals the perpendicular and half the base ' 




Fig. 


15. 




C B 


C 


\ / 
\vi> / 

\/ 




/ 


/\ 


/\ 


. 


/ . \ 


/ 
/ 0? 


\ 



INCREASE OF TRAVEL. 71 

The preceding method will decide the question for any- 
one place, but the following plan may be resorted to for 
the purpose of marking out on the map the entire area, 
from within which travel may be expected to be attracted 
to make use of the improved road. 

Let AB repre- 
sent a portion of 
the improved 
road, lying be- 
tween the two 
points A and B, 
at which cross- 
roads come in. 
It is required to 
fix the points 
C, C, D, D, so 

that lines drawn DAD" 
from C and C to A, and from D and D to B, shall define this 
tributary area. BC or AD is to be found in terms of AB ; 
i. e. X in terms of n. 

By the preceding investigation, 

But in the right-angled triangle ABC> 

m = v/ (a;= -f nl) 
Substituting in first equation, we get 

whence is obtained the value, 
x-=.\n. 
Therefore from A and B set off, at right angles to AB, BC, 
and AD, each equal to | AB ; join AC and BD ; and the area 
included will be that within which it would cost less for the 
inhabitants to use the improved road, though with increased 
distance, than to pursue the direct but unimproved road.* 

* Lccount, Treatise on Railways, p. 12. 



72 THE LOCATION OF ROADS 



CHAPTER II. 



THE LOCATION OF ROADS. 



" I do not know that I could suggest any one problem to be proposed t(V 
an engineer, which would require a greater exertion of scientific skill ani 
practical knowledge, than laying out a road." — Dr. Lardner, in 1836. 

The location, or laying out, of a road, consists in de- 
termining and marking out on the ground those points 
through which the road should pass, in order to satisfy, 
as nearly as possible, the requirements of " what a road 
ought to be." 

These requirements, so far as they affect the location 
of a road, are, in recapitulation, as follows : 

As to direction — that the road should be as straight as 
possible, but that straightness should be considered sub- 
ordinate to easiness of grade. 

As to slopes — that the road should be as level as possi- 
ble ; that it should avoid unnecessary undulations ; and 
that its slopes should not exceed 1 in 30, nor fall below 
1 in 125. 

As to cost — that the amount of excavation, embank- 
ment, mechanical structures, &c., should be the least 
which will make the road " what it ought to be," in refer- 
ence to the quantity of traffic upon it. 

If the country through which the road is to pass should 
be a plain of uniform surface, a straight line joining the 
two termini, and running along the surface of the ground, 
would satisfy all these conditions at once. In most cases, 



REQUIREMENTS OF A PERFECT ROAD. 73 

however, the ground is so uneven, hilly, and undulating, 
as to present very great difficulties in the way of a proper 
location. The shortest line would pass over the tops of 
hills and the bottoms of valleys, and would thus be often 
so steep as to be impassable. The most level line would 
often increase the distance too much by its necessary 
windings ; as would also the cheapest line, which seeks to 
avoid all cuttings and fillings. It is generally impossible 
to unite all these requirements, and to secure all the good 
qualities and valuable attributes of the ideally perfect 
road ; and the best line will therefore be a compromise 
between them all. Great skill is consequently required 
to select the best possible line among these conflicting 
claims, and this skill is more often needed in our new and 
rapidly expanding country than in England and other 
long-settled regions, where the lines of all important roads 
have been long since established ; though even there 
many miles of old roads are yearly abandoned, and new 
lines substituted for them, in order to make a sYwht saving- 
of distance, or to diminish the height to be overcome. 

Tivo distant points of departure and arrival being 
given, it is required to determine the best line for a road 
connecting them. 

In many cases the best general route for the desired 
road can be determined with perfect certainty without 
going upon the ground, by simply examining a map of 
the district upon which merely the courses of the streams 
are laid down. From them an instructed and skilful eye 
can deduce all the elevations and depressions of the coun- 
try with great precision and accuracy. To do this, how- 
ever, requires a knowledge of so much of Physical Geog- 
raphy as explains the manner in which nature has dis- 
posed the inequalities of the surface of the earth. 



74 THE LOCATION OF ROADS. 



1. ARRANGEMENT OF HILLS, VALLEYS, AND WATER-COURSES. 

Hills and valleys at first glance appear to the ignorant, 
and even to the better informed, to be utterly without 
system, order, or arrangement ; but they have in reality 
been disposed by nature with a great degree of symmetry, 
and their forms and positions are found to be the result 
of the uniform action of natural lavi^s, and to be capable 
of being traced out and understood with comparative 
ease. 

Hills being the great antagonists and natural enemies 
of the road-maker, he must endeavor to find out their weak 
points, and to learn where he can best attack and pene- 
trate them, and most easily overcome their opposition to 
his improvements. Water-cowses being his guides and 
chief assistants, he must study their habits and principles 
of action, and learn what are the causes which produce 
their seeming vagaries of direction. 

Hills are most usually found constituting chains, or 
ridges, though sometimes collected in groups, and at 
others detached, or isolated. The chains are usually 
made up of several parallel ranges, and often send forth 
branches or spurs in transverse directions. Sometimes 
they are merely the slopes of a table-land in which their 
summits merge. To form a proper conception of a range 
of hills, imagine in the midst of a plain an elongated mass 
of the form of the roof of a house. The two faces of 
this represent the slopes of the range ; their intersection 
is the ridge, their bases are theyee^, the distance from one 
foot to the other is the breadth, and from one extremity to 
the other the length ; the vertical elevation of the ridge 
above either foot is its relative height, and above the sea 



LINE OF GREATEST SLOPE. 



Y5 



ils absolute height. All water which falls upon the slopes 
descends thence in a well-defined track which corresponds 
with the line of greatest slope, the direction of which it is 
therefore important to determine. 




LINE OF GREATEST SLOPE. 

If the ridge AB of a 
range of hills be horizontal, 
and its opposite slopes in- 
clined planes cutting each 
other in that horizontal line, 
a spherical body, allowed to roll down freely from any point 
C of the ridge, will descend in the line CD at right angles to 
the horizontal line AB ; this line CD being its nearest pos- 
sible approach to the vertical line in which it tends to move 
in obedience to the law of gravity. CD is therefore the line 
of greatest slope, and consequently of quickest descent. It is 
this line which water tends to follow in its search for the short- 



Fig. 17. 



est path of descent. 

If the ridge AB be in- 
clined, the path down which 
the sphere will roll is no 
longer CD at right angles to 
AB, but another line CE, 
diverging in the direction of 
the slope of the ridge. To 
determine its precise posi- 
tion, from any point C, Fig. 
18, let fall a vertical line CV, 
and, from any point F of this 
vertical, raise a perpendicu- 
lar to the plane of the slope, 
meeting it in E. Draw CE, 
and it will be the line of 
greatest slope required ; for 
it is at the least possible distance from the vertical line CV. 




76 THE LOCATION OF ROADS. 

The same result might be otherwise obtained by raising at 
C a perpendicular to the plane of the slope, and from any point 
therein letting fall a vertical line, which will intersect the 
slope at some point E, which is to be joined to C as before. 

When the slopes are not planes, the constructions are more com- 
plicated, as the " lines of greatest slope" then become curves.* 

The waters which have fallen upon the mountain-tops 
from time immemorial, have hollowed out for themselves, 
or have adopted for their passage, channels which follow 
the lines of greatest slope, whose directions we have just 
investigated. In descending the slopes of a range of hills, 
they thus form " principal" valleys, the directions of which, 
as we have seen, are perpendicular to the ridge when it is 
horizontal, and, when it is inclined, share its general in- 
clination. These streams thus divide the range or chain 
into rainifications or branches, having approximately the 
same direction as themselves. The line in which the 
opposite slopes of two of these adjoining " branches" in- 
tersect each other, and which thus marks out the lowest 
line of a valley, is called a thalweg.] The foot of one of 
the opposite slopes which enclose a valley is generally 
parallel to the foot of the other in all its sinuosities, a 
projecting point of the one corresponding to a receding 
cavity in the other. This symmetry is, however, some- 
times replaced by alternate widenings and contractions. 

The main ridge is cut down at the heads of the streams 
into depressions called gaps, or passes ; the more ele- 
vated points are called peaks. They are respectively the 
origins of the valleys and of the branches on both sides of 
the principal slope. In the gaps are often found swamps, 

** Gayffier, p. 3. 

t A German word, (signifying " the road of the valley") which has been 
naturalized in the French language, and might be conveniently added to 
our engineering vocabulary in English. 



HILLS, VALLEYS, AND WATER-COTJRSES. 77 

fed by ihe rain which falls on the peaks between which 
they lie. In these the streams take their rise, and thence 
run in contrary directions down the opposite slopes of the 
ridge. The intermediate point, from which they start and 
diverge, is called the culminating point of the ridge. 

Thus the " Notch" of the White Mountains is the " cul- 
minating point" from which diverge the Saco and the Am.- 
monoosuc, the one emptying into Long-Island Sound and 
the other into the Atlantic, So, too, from the various cul- 
minating points in the Alleghany chain, streams run, on 
the one side towards the Atlantic, and on the other to the 
great lakes and to the Mississippi. From the culminating 
points of the Rocky Mountains, the slightest impulse would 
turn the nascent stream either into the head-waters of the 
Missouri and thence into the Gulf of Mexico, or into the 
head-waters of the Columbia and thence into the Pacific 
Ocean. The same phenomena, on a miniature scale, are 
repeated on every ridge after every shower. 
. A river of the largest class marks the lowest points (or 
the thalweg) of a " principal" valley. On each side of it is 
a bounding ridge, which is itself pierced by " secondary" 
valleys, through each of which runs a stream of less mag- 
nitude, its waters emptying into the first-named river, of 
which it is a tributary. The ridges which form the val- 
leys of each of these lateral streams are in their turn fur- 
rowed by valleys of the third class ; their banks by the 
valleys of streams of still less importance ; and so on. 

The " principal" valley is a trunk, from which, and 
from one another, the lesser valleys and strean:is ramify, 
like the branches of a tree, or like the veins of the body ; 
meeting it at angles approaching more nearly to a right 
'angle in proportion as the ridge of the slope which they 
furrow approaches to a horizontal line. 



78 



THE LOCATION OF ROADS 
Fij. 19. 




INFERENCES FROM THE WATER-COURSES. 

"We thus see how an accurate map of the streams of any 
district may enable us to deduce from them the position 
of the valleys, their lowest points, and the lines of greatest 
slope ; for with these the water-courses coincide. The 
position of the ridges which form the valleys is a necessary 
corollary, as well as their lines of greatest slope. 

Havmg determined these, we can profit by the follow- 
ing fundamental principles : 

1. If a principal ridge is met by two secondary ridges at 
the same point, the point of meeting is a maximum of height. 

2. If a principal ridge is met by two thalwegs at the . 
same point, the point of meeting is a minimum of height. 

3. If a principal ridge is met at the same point by a 
secondary ridge and a thalweg, nothing can be inferred.* 

The following examples! show more in detail some of 
the inferences which may be drawn from the map : 

If, on any portion of a map, the Y\g. 20. 

streams appear to diverge from any 
point, as A, that point must be the 
common source of the streams, and 
therefore the highest part of that re- 
gion. 

The converse is likewise true : if 
the streams all converge towards some 




* JuUien, ii. 293. 



t Mahan, p. 278. 



INFERENCES FROM WATER-COURSES. 



79 



point, as B, that will be the lowest 
spot of the district embraced with- 
in the map. 

If two streams are seen to flow in 
opposite directions from the same^ 
point, as C, it may be inferred that 
this spot is at the head of the respec- 
tive valleys of these streams, and 
supplies them with water, and that it 
must be fed by higher ground beside 
it ; or, in other words, that there is a 
ridge of hills separating the heads of 
the two streams, and that there is a 
depression or indentation in this ridge 
at the point C, which is therefore the 
natural and proper location for a road 
connecting the two valleys. 

If two streams are parallel to each 
other, and flow in the same general 
direction, this circumstance simply 
indicates that the ridge which divides 
them has the same general inclina- 
tion and direction as the streams. 
But if any of their smaller tributaries 
approach each other at their sources, 
as at D, this indicates a depression 
of the main ridge at that point, and 
marks it out as the lowest and easi- 
est spot for the crossing of a road, 
as in the preceding case. 

If two streams have been flowing 
in parallel courses, but at a certain 
point E diverge from each other, 



Fig. 21. 




Fiff. 22. 




Fig. 


23. 




Y 


\ 


^ 


A D 


^ 


u 


y^ 


^ 


\ 



Fiff. 24. 




80 



THE LOCATION OP ROADS. 




that spot is the lowest point of the Fig. 25. 

ridge between them. 

If two streams are generally par- 
allel in their courses, but flow in 
opposite directions, the low points in 
the ridge between them will still be 
shown by the approach to each other, 
as at F, of the branches or secondary 
streams ; or by the principal streams approaching each 
other at any point, as at G. 

Having thus become acquainted, by the aid of the 
map, with the principal features of the ground, we are 
prepared to plan, if not the precise location of the road, at 
least the proper course for the preliminary explorations 
upon the ground. Long lines of road usually follow the 
valleys of streams, and thus secure moderate grades and 
find the lowest passes of the ridges to be crossed. In this 
way the Simplon road crosses the Alps, by ascending the 
valley of the Saltine to its head, and then descending that 
of the Doveria. So, too, the Boston and Albany railroad 
finds an easy grade from Worcester to Springfield in the 
valley of the Chickapee river, and then winds through 
the mountains, up the valley of the Westfield, till it 
reaches the head-waters of the Housatonic upon the other 
side of the ridge. The Ulica and Schenectady railroad 
never quits the valley of the Mohawk. In short, all roads 
strive to avail themselves of such facilities. If they can- 
not, and if the map shows that their general course is 
transverse to the directions of the streams, instead of with 
them, it may be at once predicted that they will be steep 
in their ascents and descents, or exceedingly expensive 
in their construction. 

These principles having been established, and all pos- 



RECONNAISSANCE. 81 

sible information obtained from the map, the Reconnais- 
sance may be commenced. 



2. REOONIirAISSANOE. ' 

This is a rapid prehminary survey of the region through 
which the road is to pass, and is generally made by the 
eye alone without instruments. It is intended to be only 
an approximation to accuracy, and to serve to determine 
through what points routes should be instrumentally sur- 
veyed. The road-maker must examine the country, map 
in hand, visit and identify the points selected on the map, - 
and see whether his closet decisions have been correct. 
He must go over the ground backward and forward in op- 
posite directions, for it will often appear quite different, and 
convey very dissimilar impressions, according to the point 
from which it is viewed. Thus, a hill which one is de- 
scending may seem to have a very easy slope, while it 
may appear very steep to one ascending it. No time or 
labor should be spared in these first explorations, as they 
will save much expense in the subsequent surveys, which 
in their turn should be thoroughly executed, to secure the 
route most economical in construction. Indeed, the sur- 
veyor should become as perfectly acquainted with the 
face of the country as if he had passed his hand over 
every foot of it. 

Certain points, called " ruling" or " guiding" points, 
will be found, through which the road must pass ; such 
as a low gap in a range of hills, a narrow part of a river 
suitable for a bridge, a village, &c. But a road which is 
to be a thoroughfare between two places of great trade, 
should not be turned from its direct course to accommo- 
date a small town, taxing for its benefit all who travel upon 

6 



82 



THE LOCATION OF ROADS. 



the road. " The greatest good of the greatest number" 
is here the rule. Still less should individual interest be 
allowed to operate, and the general interest of the com- 
munity be sacrificed to the convenience or caprice of a 
single person. The permanent benefits to future genera- 
tions should never be made subordinate and subservient 
to temporary and personal advantages. 

Between these " ruling" points, the straight line joining 
them is to be marked out. The route adopted must vi 
brate on each side of this line, like an elastic cord, con 
tinually tending to coincide with it, except when deflected 
to the right or to the left by weighty reasons, such as the 
accidents of the ground supply. Thus, a swamp, which 
would render necessary an expensive causeway, is a suf- 
ficient cause for a wide deviation of the road to avoid it. 
The disadvantages of straight lines, which encounter and 
run over hills, have been explained in the preceding chap- 
ter. In the accompanying Fig. 26. 
figure the upper sketch 
shows a plan, or map- 
view, of two roads, the 
one ACB over a hill, and 
the other ADB around it ; 
and the lower sketch 
shows a profile, or side- 
view, of the respective a ^ 
heights of the same lines. 

When there are many small valleys or ravines, with 
projecting spurs and ridges intervening, nistead of making 
the road wind on the level ground, and follow all its sinu- 
osities, as, ACCCCB, in the next figure, it will be better 
to make a nearly straight line, as ADDDB, cut through the 
projecting points in such a way that the earth dug out 




RECONNAISSANCE. 



83 



shall just suffice to fill the hollows. The gain by saving 
of distance may balance the cost of cutting and filling. 



Fiff. 27. 




When the route follows the valley of a stream, it may 
conform to its sinuosities, if the turns are not too abrupt, 
and if the cuttings and fillings on a straighter line would 
be too expensive, but should approximate to the latter 
plan, if the importance of the road and the funds at com- 
mand will justify the increased cost. The former plan, 
however, generally gives the cheapest and most level 
route ; and guided by this principle a blind man was for a 
long time the very best layer out of roads in the hilly re- 
gions of Yorkshire and Derbyshire. He followed the 
streams closely, and when they made too sharp bends, 
he sought in these arcs the straightest chords which 
passed over practicable ground. 

When a valley is to be crossed, the route should gen- 
erally deviate from the straight line ACB, (Fig. 28) and 
curve towards the head of the valley ADB, which there is 
usually shallower and narrower. If it deviated in the other 



84 



THE LOCATION OF ROADS. 




k- 



direction, as AEB, itwould 
increase the depth and 
width to be filled up, as is 
shown by the correspond- 
ing profiles. 

But sometimes the two A 
sides of the valley ap- 
proach each other at some 
point lower down, so as 
to render the space be- 
tween their banks narrow- 
er though deeper ; and if 
on measurement this area 
is found on the whole to be lessened, so as to require less 
embankment, the road should cross at that point instead 
of higher up. 

Another case in F'?- 29- 

which a valley may, 
with advantage, be 
crossed down stream, 
is when in that part 
of the valley are found 
detached or isolated 
hills and ridges, as E 
and F, which may 
cause a great saving 
of embankment, on 
the fine AEFB, com- 
pared with either the 
straight route ACB, or the up-stream one ADB, as is 
shown in the accompanying plan and profile, in which the 
same letters refer to corresponding lines. 

When a road is to join two places on the opposite sides 



^m 

'"*^ 




RECONNAISSANCE. 85 

of a ridge, we can profit by the observation that the 
streams, by the approach of their sources, show the low- 
est points of the ridge ; and of the various passes thus 
indicated, we should choose that one, the valleys of the 
streams from which run as nearly as possible in the di- 
rection of the required line ; and that one, also, which 
has the most uniform inclination — not easy at the foot 
and steep towards its summit, as is often the case. 

When a road is to join two places situated on the same 
side of a mountain ridge, hut half way down its side, a 
straight line between them would cross, in their deepest and 
widest parts, all the " principal" valleys which run down 
from every gap. One of two other plans must then be 
adopted ; either to ascend, and carry the road, with neces- 
sary windings, at the level of the culminating points of 
the gap, where the valleys have only begun to be hollowed 
out ; or to carry it at the foot of the ridge, where the val- 
leys have run out to nothing, and merged themselves un- 
distinguishably in the plain. Either plan, in spite of the 
initial and final ascent and descent, is preferable to the 
direct line. 

Fig. 30. 

D 




E 

The respective profiles of the three plans would be 
somewhat as represented in the figure, in which ACB is 
the first plan, ADB the second, and AEB the last. The 
last line is generally taken, because there are more inhab- 
itants at the foot of the ridge. It would properly run near 
the line of separation between the uncultivated slopes and 
the ploughed fields. 



86 THE LOCATION OF ROADS. 

The location of a road is also influenced by ihe. geology 
of a district, which must therefore be carefully studied 
This science will make known the probability of finding 
rock on cutting deep into a hill proposed to be crossed ; 
in which case the cutting should be avoided, if possible, 
by a different location of the line. It will also determine 
the dips of the strata to be cut into, the angle at which 
they will stand, and their liability to slip ; and therefore 
through which the line may best pass. If the road is to 
be covered with broken stone, or to be paved, a know- 
ledge of the locality of the best materials might cause a 
line approaching it to be preferred to one which left it at 
a distance. 

The Reconnaissance is to be made in accordance with 
the principles which have been enunciated, obtaining all 
needful information from the residents of the region to be 
examined, and the details of its general course are to be 
marked out on the ground, thus establishing " Approxi- 
mate" or " Trial" lines. In a wooded country this is done 
by " blazing" the trees in the line selected, (removing a 
chip from their sides with an axe ;) and in a cleared coun- 
try by driving stout stakes at the most important points of 
the line, such as all changes in its direction, and in the 
slope of the ground. 

3. SURVEY OF A LIKE. 

When the different portions of a proposed line have 
been thus marked out, in order to form an accurate opin- 
ion of its merits, it is necessary to measure — 

1. Its distances. 

2. Its directions. 

3. Its heights. 



11 



MEASUREMENT OF DISTANCES. 87 

MEASUREMENT OF DISTANCES. 

The length of a straight hne, that is, the distance be- 
tween its extremities, may be approximately estimated in 
a variety of ways, without the delay of actual measure- 
ment in detail. 

Sound is a well-known means. Its velocity is 1100 
feet per second at the temperature of freezing.* If a gun 
be fired -by an assistant at one end of a hne, an observer 
at the other end, by counting the seconds which intervene 
between seeing the flash and hearing the report, and mul- 
tiplying their number by 1100, can estimate the distance 
with considerable accuracy. If he have not a watch with 
a second-hand, he can at once make a portable pendulum, 
by fastening a pebble to a string, and making it swing in 
regular vibrations, each of which will be performed in an 
exact second, if the string be 39i inches, long ; in half a 
second, if it be 9| inches long ; and in a quarter second, 
if its length be 2| inches. 

This method is best adapted for considerable distances, 
in which there are good points for observation, such as 
the hills on the two opposite sides of a wide valley. 

For shorter distances, the distinctness with which dif- 
ferent objects can be seen, is an approximate guide. Thus 
the windows of a large house can generally be counted at 
the distance of 3 miles ; men and horses can just be per- 
ceived as points at about 1^ miles ; a horse is clearly dis- 
tinguishable at I mile ; the movements of a man at 
I mile ; and a man's head is plainly visible at g- mile.f 

* For each degree of Fahrenheit above 32°, add one-half foot, and for 
each degree below, subtract one-half foot. A temperature of 60° would 
therefore give 1100 -f-^^ = 1114 feet per second. 

t Frome, p. 60. 



88 THE LOCATION OF ROADS. 

The Arabs of Algeria define a mile as " ihe distance at 
which you can no longer distinguish a man from a wo- 
man." These distances of visibility will of course vary 
somewhat with the state of the atmosphere, and still more 
with individual acuteness of sight, but each person can 
modify them for himself. 

For still less distances, an easy method is to prepare 
a scale, by marking off on a pencil what length of it, when 
it is held off at arm's length, a man's height appears to 
cover at different distances (previously measured with ac- 
curacy) of 100, 500, 1000 feet, &c. • To apply this, when 

Fig. 31. 




a man is seen at any unknown distance, hold up the pen- 
cil at arm's length, making the top of it come in the line 
from the eye to his head, and placing the thumb nail in 
the line from the eye to his feet. The pencil having been 
previously graduated by the method above explained, the 
portion of it now intercepted between these two lines will 
indicate the corresponding distance. 

If no previous scale have been prepared, and the dis- 
tance of a man be required, take a foot-rule, or any meas- 
ure minutely divided, hold it off at arm's length as before, 
and see how much a man's height covers. Then know- 
ing the distance from the eye to the rule, a statement by 
the Rule of Three (on the principle of similar triangles) 
will give the distance required. Suppose a man's height, 
of 70 inches, to cover 1 inch of the rule. He is then 70 
times as far from the eye as the rule ; and if its distance 



MEASUREMENT OF DISTANCES. 89 

DC 2 feet, that of the man is 140 feet. Instead of a man's 
height, that of an ordinary house, of an apple-tree, the 
length of a fence-rail, &c., may be taken as the standard 
of comparison. 

Quite an accurate measurement of a line of ground may 
be made by loalking over it at a uniform pace, and count- 
ing the steps. It is better not to attempt to make each 
of the paces three feet, but to take steps of the natural 
length, and to ascertain the value of each by walking 
over a known distance, and dividing it by the number of 
paces required to traverse it. An average length is 32 
inches. An instrument, called a pedometer, has been 
contrived, which counts the steps taken by one wearing 
it, without any attention on his part. It is attached to the 
body, and a cord, passing from it to the foot, at each 
step moves a toothed wheel one division, and some inter- 
mediate wheelwork records the whole number upon a dial. 

These methods are all approximations. For more ac- 
curate measurements a chain is employed. The usual sur- 
veyor's or Gunter's chain, is 66 feet or four rods long, and 
is divided into 100 links ; but for the measurement of 
distances only, without reference to areas in acres, a chain 
of 50 or 100 feet is much preferable. 

When obstacles are encountered on the line, rendering 
a direct measurement impossible, such as a house, a 
pond, a river, &c., resort must be had to some of the 
many ingenious contrivances to be found in the special 
treatises on surveying and engineering field-work. Two 
only of the best, which have the advantage of requiring 
no calculations, will be here given. 

When the obstacle is one around which we can pass, 
such as a house or a pond, the following plan may be 
adopted. Let AE be the distance required. Measure 



90 



THE LOCATION OF ROADS, 




from A obliquely to some point C, ^'S- 32. 

past the obstacle. Measure on- 
ward in the same line, till CD is as 
long as AC. Place stakes at C 
and D. From B measure to C, 
and from C measure onward in the 
sam.e line, till CE is equal to CB. 
Measure ED, and it will be equal 
to AB, the distance required. 

When the obstacle is a river, the following is the method 
to be employed. Let AB be Fig. 33. 

the required distance. From 
A measure any line diverging 
from the river, as AD, and 
set a stake in its middle point 
C. Take any point E, in the 
line of A and B. Measure from 
E to C, and onward in the 
same line, till CF equals CE. 
Then find by trial the point 
G, which shall be at the same 
time in the line of C and B, and in the line of D 
and F. Measure the distance from G to D, which 
will equal the required distance from A to B. The 
lines which it is not necessary to measure are dotted 
in the figure. 




MEASUREMENT OF DIRECTIONS. 



Having measured the lengths of the various portions of 
the line, by whatever method will give the degree of ac- 
curacy required, their directions are also to be examined, 
determined, and recorded. 




MEASUREMENT OF DIRECTIONS. 91 

These directions "liiay be accurately determined, witli 
reference to the adjoining portions of the hnes, and there- 
fore to any given hue, by simple measurements with 
the chain, without the use of any of the usual complicated 
angular instruments. 

Let AB and BC rep- Fig. 34. 

resent two lines on the a b D 

ground, meeting at any 
angle. It is required to 

determine the change C" 

in the direction of the line BC from that of AB, i. e., the 
angle CBD, or the " angle of deflection." Set off from B 
equal distances, BC on the new line, and BD on AB pro- 
duced, and measure DC, which is the chord of the angle 
required. To find the angle numerically, take half this 
measured chord, (which equals the sine of half the angle 
to radius BC) and divide it by BC. Find in a table of 
natural sines the angle corresponding to the quotient. 
Twice this is the angle CBD required. But even this 
brief calculation is needless for putting down the line 
upon paper, as it is only necessary to describe an arc 
from B as centre With BC as radius, and to set off CD of 
the proper length, the distances being taken from any one 
scale. 

If the direction of a line be required independently of 
any other line upon the ground, it is usually referred to 
the direction of the meridian, i. e., the line which passes 
through the north and south poles of the earth. The 
compass is the readiest means of obtaining this, although, 
in addition to its other inherent defects, it gives the angle 
made by the given line with only the magnetic meridian, 
which is constantly changing, and from which the true 
meridian in most places varies considerably. 



92 



THE LOCATION OF ROADS. 




To determine the t7'ue meridian (and therefore the 
angle which any line makes with it) without the use of 
the compass, the following is a simple and sufficiently 
accurate method. On the south side of any level surface, 
erect an upright staff, shown, Fig. 35. 

in horizontal projection, at A. 
Two or three hours before 
noon mark the extremity, B, 
of its shadow. Describe an 
arc of a circle with A, the 
foot of the staff, for centre, 
and AB, the distance to the 
extremity of the shadow, foi 
radius. At about as many 
hours after noon as it had been before noon when the 
first mark was made, watch for the moment when the end 
of the shadow touches the arc at another point C. Bisect 
the arc BC at D. Draw AD, and it will be the true me- 
ridian, or north and south line, required. 

For greater accuracy, describe several arcs, mark the 
points in which each of them is touched by the shadow, 
bisect each, and adopt the average of all. The shadow 
will be better defined, if a piece of tin with a hole through 
it be placed at the top of the staff, as a bright spot will 
thus be substituted for the less definite shadow. Nor 
need the staff be vertical, if from its summit a plumb- 
line be dropped to the ground, and the point which this 
strikes be adopted as the centre of the arcs, through which 
the meridian line AD is. finally to be drawn.* 



* For the method of determining the true meridian by the north stM, 
see Davies' Surveying, p. 127. 



MEASUREMENT OF HEIGHTS. 



93 



Fig. 36. 
c 



MEASUREMENT OF HEIGHTS. 

The relative heights of the different points, at which 
ihe Hne changes its slope, are next to be determined. 
The operation required for this purpose is called level- 
ling. It consists in finding how much each of these 
points is below any level line. The difference of their 
distances below it (measured perpendicularly to it) is the 
difference of their heights. The first step, then, is to 
discover means of getting a level line at any point desired. 

The principle, that a level line is everywhere perpen- 
dicular to the direction of gravity, furnishes the first 
method. Upon it depends the well-known " Mason's 
level,'''' in which a 
straight edge AB is 
'* level," or horizontal, 
when a line CD, ex- 
actly at right angles 

to it, is covered by a 

plumb-line attached to A 
its upper extremity C. 

As this position of the level line is inconvenient, in 
practice, for long sights, by inverting the instrument we 
get the " Plumb-line level." To construct it, at the mid- 
dle of a straight edge, at- Fig. 37. 

tach a bar, so that a line -^-t- ~r , 

drawn through its middle 
is exactly at right angles to 
the straight edge. From 
the point of meeting sus- 
pend a plumb-line. Turn 
the instrument till the ^ 

plumb-line covers the line drawn on the bar. Then will 



94 



THE LOCATION OF ROADS. 




the Straight edge be a level line, and by looking over its 
surface, or across sights, placed at equal heights above its 
ends, this level line may be produced by the eye, so as to 
pass over any point to which the straight edge is directed. 

A modification of the Fig. 38. 

plumb-line level, which 
has the advantage of be- ^. 
ing self-adjusting, is call- 
ed the " Pendulum lev- 
el.'" As before, a straight 
edge and a bar are fixed 
at right angles to each 
other, but a heavy weight at the lower extremity of the 
bar keeps it always vertical, and, consequently, the 
straight edge always horizontal. The whole apparatus 
is suspended by a ring from the junction of three legs 
which move on pivots, so as to form a steady support on 
the most uneven ground. A " tripod''' of this sort is gen- 
erally employed for the support of all the instruments of 
surveying. 

The " A lever is a 
portable and conveni- 
ent modification of the 
mason's level. The 
legs AB, AC turn on a 
hinge at A, as does the 
bar DE at E, so that all 
three may. be folded up 
into a stout rod. When 
the plumb-line corre- 
sponds with the middle of the bar DE, the feet of the in 
strument are on the same level At F and G are fixed 
two sights, at equal distances from the feet, so that 




LEVELLING INSTRUMENTS. 



95 



whei! the latter are level, the line, obtained by looking 
through these sights, is level also. The use of the other 
divisions on .he bar DE Vi^ill be explained under the head 
of " Grades."* 

Another simple instrument depends upon the principle 
that " vi^ater always finds its level." If a tube be bent up 
at each end, and nearly filled with water, the surface of 
the water in one end will always be at the same height as 
that in the other, however the position of the tube may 
vary. On this truth depends the " Water level.'''' It 
may be easily con- Fig. 40. 

structed with a 
tube of tin, lead, 
copper, &c., by 
bending up, at right 
angles, an inch or 
two of each end. 
In these ends ce- 
ment thin vials, 
with their bottoms 
broken off, so as to leave a free communication between 
them. Fill the tube and the vials, nearly to their top, 
with colored water. Cork their mouths, and fit the instru- 
ment, by a steady but flexible joint, to a tripod. 

To use it, set it in the desired spot, place the tube by 
eye nearly level, remove the corks, and the surfaces of 
the water in the two vials will come to the same level. 
Looking across them, we get the level line desired 
Sights of equal height, floating on the water, and rising 
above the tops of the vials, would give a better-defined line. 

The ^^ Spirit level" consists essentially of a curved glass 




* See Simms on Drawing Instruments, 2d edition, p. 146. 



96 THE LOCATION OF ROADS. 

tube filled with alcohol, but Fig. 41. 

with a bubble of air left 
within, which always seeks 



=irrj^ 



the highest spot in the tube, and will therefore by its 
moven:ients indicate any change in the position of the 
tube. To prepare the tube for use, it is placed with its 
convexity uppermost, and supported either in a block, or by 
suspension ; and when the bottom of the block, or the 
sights at each end of it, coincide with some level line 
previously established, marks are made on the tube at the 
extremities of the air bubble. The instrument is then 
ready for use ; for whenever the bubble, by raising or 
lowering one end, has been brought to stand between the 
original marks, (or, in case of expansion or contraction, at 
equal distances on either side of them) the sights will be 
on the same level line. 

When, instead of the sights, a telescope is made parallel to 
the level, and various contrivances to increase its delicacy and 
accuracy are added, the instrument becomes the engineer's 
spirit-level, and is out of the reach of the unprofessional read- 
ers for whom this volume is chiefly designed.* The same is 
the case with the " French reflecting level." 

By whichever of these various means a level line has 
been obtained, the subsequent operations in making use 
of it are identical. Since the " water level" is easil)'- 
made and tolerably accurate, we will suppose it to be em- 
ployed. Let A and B represent the two points, the differ- 
ence of the heights of which is required. Set the instru- 
ment on any spot from which both the points can be seen, 
and at such a height that the level Ime will pass above the 
highest one. At A let an assistant hold a staff graduated into 
feet, tenths, &c. Turn the instrument towards the staff, 

* For its description and adjustments, seo Davies' Surveying, p. 140. 



LEVELLING. 



97 



look along the level 
line, and note what 
division on the staff 
it strikes. Then 
send the staff to B, 
direct the instru- 
ment to it, and note 
the height observed 
at that point. If 
the level line pro- 
duced by the eye 



Fig. 42. 




B 

6 feet 
The 



passes 2 feet above A and 
al?ove B, the difference of their heights is 4 feet 
absolute height of the level line itself is a matter of 
indifference. If the height of another point, C, not visible 
from the first station, be required, set the instrument so as 
to see B and C, and proceed exactly as with A and B. 
If C be found to be 3 feet above B, it will be 4 — 3 = 1 
foot below A. If C be 1 foot below B, as in Fig. 43, it 
will be 4-f- 1= 5 feet below A. The comparative heights 

Fiff. 43. 




of a series of any number of points, can thus be found in 
reference to any one of them. 

The beginner m the practice of levelling may advan- 
7 



98 



THE LOCATION OF ROADS. 



tageously make in his "field-book" a sketch of the heights 
noted, and of the distances, putting down each as it is 
observed, and imitating, as nearly as his accuracy of eye 
will permit, their proportional dimensions.* But when 
the observations are numerous, they should be kept in a 
tabular form, such as that which is given below. The 
names of the points, or " stations," whose heights are de- 
manded, are placed in the first column ; and their heights, 
as finally ascertained, in reference to the first point, in the 
last column. The heights above the starting point are 
marked +, and those below it are marked — . The back- 
sight to any station is placed on the line below the point 
to which it refers. When a back-sight exceeds a fore- 
sight, their difierence is placed in the column of " as- 
cents ;" when it is le^s, their difference is a "descent." 
The following table represents the same observations as 
the preceding sketch, and their careful comparison will ex- 
plain any obscurities in either. 



stations. 


Distances. 


Back-sights. 


Fore-sights. 


Ascents. 


Descents. 


Total Heights. 


A 












0.00 


B 


100 


2.00 


6.00 




— 4.00 


— 4.00 


C 


60 


3.00 


4.00 




— 1.00 


— 5.00 


D 


40 


2.00 


1.00 


+ 1.00 




— 4.00 


E 


70 


6.00 


1.00 


+ 5.00 




+ 1.00 


F 


50 


2.00 


6.00 




— 4.00 


-3.00 


15.00 


18.00 


— 3.00 



The above table shows that B is 4 feet below A ; that 
C is 5 feet below A ; that E is 1 foot above A ; and so 
on. To test the calculations, add up the back-sights 



* In the figure, the hmits of- the page have made it necessary to con- 
tract the horizontal distances to one-tenth of their proper proportional size. 



LEVELLING. 99 

and fore-sights. The difference of the sums should equal 
the last " total height."* 

The level hne obtained by any of these instruments 
is a tangent to the surface of the earth, and therefore di- 
verges from the surface of standing water, which presents 
a curve corresponding to that of the earth. The differ- 
ence between the lines of true and apparent level, is 8 
inches at the distance of a mile ; but since it varies as the 
square of the distance, it is very insignificant in sights of 
ordinary length, (one-eighth of an inch for a sight of one- 
eighth of a mile) and may be completely compensated by 
setting the instrument midway between the points whose 
difference of level is desired ; a precaution which should 
always be taken, when possible. If the ground renders 
sights of unequal length unavoidable, a balance should be 
struck as soon as possible, by adopting corresponding 
mequanties in the contrary direction. 

The heights observed along the length of the road, which 
give its " longitudinal section," should be taken at every 
change of slope ; and at every hundred feet, when the line 
is finally located. 

It is also necessary to take them at right angles to its 
length, in order to obtain the " transverse" or " cross sec- 
tions.'''' These are required for the subsequent calcula- 
tions of the " cutting and filling," and to enable the engi- 
neer to see what would Pi 44_ 
be the effect upon these, ^^ 
of moving the line to the ^^^^^^ ^i 
right or to the left. The ^^^^-"^^ 30 
right page of the note- ^^^--'"''^ §1 
book is usually devoted, ' 

* For another form of Levelling^ Field-book, see page 145*. 



lOO THE LOCATION OF ROADS. 

in part, to the cross-sections, taken in reference to any 
station, as B. In this example, on the right, the ground 
rises 10 feet in going out 30 ; on the left, it falls 20 in a 
" distance out" of 50. 

These cross-sections should be taken at every change 
of longitudinal slope. At every change of slope trans- 
versely, single heights and " distances out" should be 
taken. The future calculations of cubical contents will 
be facilitated by observing the following rules : — 

1. Take a cross-section whenever either edge of the 
road passes from excavation to embankment, or vice 
versa. 

2. When the road is partly in excavation and partly in 
embankment, ascertain the " distance out" at which the 
grade, or level of the base, cuts the surface of the ground. 

3. Take heights at each edge of the base, i. e. at dis- 
tances on each side of the centre line, equal to the half 
width of the base of the road. 

4. Take the intermediate cross-sections at some deci- 
mal division of 100 feet. 

The Mountain Barometer is an instrument of great value 
for the rapid determination, with approximate accuracy, of the 
heights of the leading points in an extensive district of country.* 

The temperature of boiling water supplies another easy 
means of approximation. The degree of heat at which water 
boils diminishing as the height increases, tables have been 
constructed from observation, with the aid of which the height 
of a place may be calculated from the temperature at which 
water there boils.f 

* See Simms on Mathematical Instruments. 
t See Silliman's Journal, 1846, pp. 134-5. 



MAPPING THE SURVEY. 101 



4. MAPPING THE SURVEY. 



The lengths, directions, and heights of the different 
portions of the hne having been ascertained, they are next 
to be represented on paper, in such a vv^ay as to convey to 
an instructed eye a complete idea of the ground over which 
the route passes. This idea will be as accurate as could be 
obtained from actual examination, and much more easily 
embraced by the mind ; the details being made subordinate 
to the leading features. 

The mapping of a line comprehends two distinct 
branches : 

1. The plot. 

2. The profile. 



THE PLOT OF A LINE. 



This represents the lengths and directions of the differ- 
ent portions of a line, projected on a horizontal plane, as 
they would be seen by an eye looking down upon them 
from a great height directly above them. If the lengths 
have been measured horizontally, as is usual, they will 
require no farther reduction. Before commencing the 
plot, its " scale" must be determined, i. e., what propor- 
tion the representation is to bear to the reality, or how 
many feet of the line each foot of the plot is to represent. 
If one foot of the plot represent 1000 feet of the line, 100 
feet of the latter will occupy one tenth of a foot on the 
plot, and so on. Any convenient scale may be assumed, 
but must be carefully preserved unchanged in the same 
plot. The changes in the direction of the line, or the 
angles of deflection of its adjacent parts, may be most 
easily laid down, as explained on page 91, by describing 
an arc from the angular point with the same radius used 



102 THE LOCATION OF ROADS. 

on the ground, (taken to the proper scale) and setting oflf 
on the arc, as a chord, the proper distance measured in 
like manner. 

If the deflection had been measured by an angular in- 
strument, (which, however, the preceding method dis- 
penses with) it would have been laid down on the paper 
by a " protractor," the most usual form of which is a 
small brass semicircle, divided into degrees similar to 
those on the instrument. 

Upon the plot, it is usual to represent the hills and val- 
leys in the vicinity of the line ; but since they are supposed 
to be seen horizontally projected in a " map-view," as they 
would appear to an eye looking down upon them from an 
infinite height, they cannot be drawn with the rises and falls 
of the front view in which we usually see them, but must 
be represented by some artificial and conventional method. 
They are accordingly supposed to be cut by a number of 
equidistant horizontal planes, and the horizontal " contour 
curves" of intersection to be drawn upon the map, the in- 
tervals between them being filled up by short hatchings 
perpendicular to the curves.* Hills, represented on these 
principles, are indicated by numerous diverging lines, 
shorter, nearer, and heavier, in proportion as the hill is 
steeper, and vice versa. See the examples on pages 83-4. 

All water-courses must also be carefully represented on 
the plot ; and the nature of the surface, whether pasture, 
ploughed land, swamp, woods, &c., together with the de- 
tached objects upon it, such as houses, mills, churches, 
&c., be indicated by certain arbitrary signs. For our 
purposes they are not necessary, but may be found, if 
desired, in any topographical manual. 

* For fuller details, see Da-ries' Surveying, Eastman's . Topography, 
Williams's Practical Geodesy, &c. 



THE PROFILE OF A LINE. 103 



THE PROFILE OF A LINE. 



This represents, to any desired scale, the heights and 
distances of the various points of a hne, projected on a 
vertical plane. It thus gives a " side-view" of its ascents 
and descents. Any point on the paper being assumed for 
the first station, a horizontal line is drawn through it ; the 
distance to the next station is measured along it to the 
required scale ; at the termination of this distance a verti- 
cal line is drawn ; and the given height of the second sta- 
tion above or below the first is set off on this vertical line. 
The point thus fixed determines the second station, and a 
line joining it to the first station represents the slope of 
the ground between the two. The process is repeated 
for the next station, &c. 

But the rises and falls of a line are always very small 
in p/oportion to the distances passed over ; even moun- 
tains being merely as the roughnesses of the rind of an 
orange. If the distances and the heights were represent- 
ed on a profile to the same scale, the latter would be 
hardly visible. To make them more apparent it is usual 
to " exaggerate the vertical scale" tenfold, or more, i. e., 
to make the representation of a foot of height ten times as 
great as that of a foot of length. Take, for instance, the 
example on page 98. Let one inch represent one hun- 
dred feet for the distances, and ten feet for the heights. 

From A draw a horizontal line. Measure on it one 
■inch, representing one hundred feet of length. Thence 
draw downwards a vertical line. Measure on it four-tenths 
of an inch, representing four feet of height. This fixes the 
point B. Join A to B. This line AB represents the 
slope of the ground. Next, along the horizontal line, 
measure six-tenths of an inch farther, representing sixty feet 



104 



THE LOCATION OF ROADS. 



Fig. 45. 




of length. Measure on a vertical line thence drawn, five- 
tenths of an inch, representing five feet of height. This 
fixes C. Join C to B. Proceed in like manner for all 
the levels. 

The distances may be written horizontally in their ap- 
propriate places, and the heights or depths of the ground 
(above or below the datum line) vertically, along the 
lines which represent them, as in the figure. 

5. ESTABLISHING THE GRADES. 

The grade of a line is its longitudinal slope, and is 
designated by the proportion between its length and the 
difference of height of its two extremities. The ratio of 
these two quantities gives it its name, as we have seen ; 
the road being said to have a grade of one in thirty when 
it rises or falls one foot in each thirty feet of length. 
When the "profile" of a proposed route has been made, 
a " grade-line" is drawn upon it (usually in red) in such 
a manner as to follow its general slope, but to average its 
Fig. 46. 




irregular elevations and depressions, as in the figure. The 
ratio between the whole distance and the height is then to 



ESTABLISHING THE GRADES. 105 

be calculated. If, as in the figure, it rise 100 in 4000, the 
grade is one in forty, flatter than our assumed limit of one 
in thirty, and the line will be a satisfactory one, if on cal- 
culation it be found that the cuttings about equal the fill- 
ings. If either be much in excess, the grade is altered to 
equalize them, as will be explained under the next head. 
But if the grade be found steeper than the limit, as when 
it ascends the face of a hill with a rise of 100 feet in 
1500, or a slope of one in fifteen, either the hill must be 
cut down, or, which is generally preferable, the length of 
the hne must be increased so as to equal 100 x 30 = 3000. 
The best method of obtaining this increased length, or 
" development," (whether by a zigzag or by a single 
oblique line) will depend upon the manner in which the 
line meets the face of the hill, whether at right angles oi 
obliquely, and should be determined by geometric con- 
structions upon the plot, such as those which follow, 
modified if necessary by the features of the ground. 

Problem. To fix the position of a line joining two given 

points, so that it shall ascend with a given grade a slope 

steeper than this grade, and shall also be the shortest possible 

line which will fulfil this condition.* 

Case 1. When the straight line joining the two points meets 

the slope at right angles. 

Yw. 47. 




106 THE LOCATION OF ROADS. 

Let A and B be the given points, and let the top and bottom 
lines of the slope to be ascended be considered parallel. Let 
mn represent the length which the road up the hill must have 
to ascend with the proper gr^de. Join the given points by a 
straight line, and between the points C and D, at which this 
line meets the top and bottom line, establish a zigzag, of a 
sufficient number of turns to make its entire length equal to 
mn, the " development" required ; which in the instance last 
supposed would be 3000 feet, the straight line CD being only 
1500. 

The road which ascends the Catskill mountain makes seven 
such zigzags or tacks. Their angles should be rounded off by 
curves, as explained in a following article on " Final Location." 
At these curves the width of the road should be increased, as 
directed on page 46. 

Case 2. When the straight line meets the slope obliquely, 
and the two given points are very distant from each other. 



Let A and B be the given points. Between the top and 
bottom lines of the slope draw a line mn at such a degree of 
obliquity as will make its length equal to the development re- 
quired, which, in the instance supposed, is 3000 feet. The 
straight line AB would be too steep between C and E. There- 
fore from the point C draw a line CD, parallel and therefore 
equal to mn. Join DB, and the line ACDB will be the one 
desired. 



ESTABLISHING THE GRADES. 107 

A zigzag between C and E would give a longer line ; for, 
comparing the parts of the line thus obtained with those of the 
other, we find AC common to both ; the zigzag CE equal to 
CD by construction ; and EB longer than DB, because farther 
from the perpendicular. 

The construction above directed is merely approximately 
true, becoming perfectly so only when the points A and B are 
infinitely distant from each other. The strict construction is 
that which follows. 

Cased. When the straight line meets the slope obliquely, and 
the two given points are near each other. 

From the given points A and B draw perpendiculars to the 
nearest edges of the slope. The line joining the feet of these 
perpendiculars will be less than, equal to, or greater than, the 
developed line mn, according to the steepness of the slope, 
and the degree of obliquity with which it is met by the straight 
line which joins the given points. Three sub-cases, requiring 
different constructions, are thus formed. 

Suh-case 1. When the line joining the perpendiculars is 
shorter than the developed line van. 

Fig. 49 




From A and B draw AC and BD perpendicular to the edges 
of the slope. Join C and D by a zigzag line, equal in length 
to the developed line mn. Then will the line thus obtained 



108 



THE LOCATION OF ROADS. 



fulfil the conditions required ; the length of the zigzag being 
equal to the necessary length mn, and the lines AC and BD 
being perpendicular to the top and bottom of the hill, and there- 
fore the shortest possible distances to it. 

Sub-case 2. When the line joining the perpendiculars is 
equal to the developed line mn. 

Fig. 50. 




Draw the perpendiculars AC and BD, as before, and join 
their feet by the line CD. Then will the line ACDB be 
shorter than any other line, (as AC'D'B, obtained by the con- 
struction of Case 2) for AC and BD, being perpendiculars, are 
the shortest possible, and CD has a constant length, wherever 
it may be placed. 

A zigzag line from C to E would not produce the shortest 
line, for the same reasons as in Case 2. 

Sub-case 3. When the line joining the perpendiculars is 
longer than the developed line mn. 

From A, Fig. 51, draw AE parallel and equal to mn. Join EB. 
From the point D (where this line intersects the edge of the 
slope) draw DC parallel and equal to AE. Join CA. Then 
will ACDB be the shortest line required. 

For, AE, being equal to mn, cannot be shortened, and EB 
is a straight line, and therefore the shortest possible line, as is 



ESTABLISHING THE GRADES, 



109 



Fig. 51. 




consequently the whole line AEDB. But this line is in the 
wrong place, and its parts require to be transported parallel to 
themselves. By this operation is formed the line ACDB, 
which has all its parts equal to those of the former line, and 
which is therefore the shortest possible. 

It might seem preferable to adopt the direct line AB, and to 
ascend the hill by a zigzag from F to G ; but this would not 
give the shortest line ; for AF and GB are longer respectively 
than AC and DB, because farther from the perpendiculars. 

When the lines AC and DB, obtained by the construction 
above directed, fall beyond the perpendiculars let fall from A 
and B upon the top and bottom of the slope, this result shows 
that this construction is inapplicable, and that the case is one 
in which it is proper to adopt the perpendiculars, and to join 
them by a zigzag of the proper length. 



Case 4. When two neighboring slopes are separated hy a 
level space; whether a valley, or a table-land on the ridge of 
a hill. 

Between the top and bottom lines of one slope draw the line 
mn, equal in length to the developed line with which that slope 
must be crossed ; and in like manner on the second slope, draw 
the line pq. 

Then from A draw AE, parallel and equal to mn. From E 
draw EF parallel and equal to pq. Join FB. The line AEFB 



110 



THE LOCATION OF ROADS. 
Fig. 52. 




is the shortest line possible, for the same reasons as was AEB 
in the preceding sub-case 3. But its parts require to be differ- 
ently arranged without changing their length, which is effected 
thus. From H draw HG parallel and equal to FE. From G 
draw GD parallel to HF, and terminating at the edge of the 
next slope. From D draw DC parallel and equal to EA. Joia 
CA by a line which will be parallel to FH. This new line 
ACDGHB is equal to the former line AEFB, and therefore is 
the shortest line required. 

If the space between the two slopes was a valley, in which 
there was a given point to be passed through, as a bridge, the 
problem would divide itself into two others, such as have been 
solved in the preceding cases. 

Grades may be approximately estimated upon the 
ground, (without measuring distances and heights) by a 
slight addition to the "plumb-line level," described on page 
93. Connect the horizontal and vertical bars by oblique 
braces. To prepare it for use, depress or elevate the 
sights, so that their line coincides with an ascent or de- 



MEASURING GRADES. 



Ill 



scent of one in thirty, or any other grade previously estab- 
lished by levehing. Mark the point at which the plumb- 
line now cuts the oblique braces. Do the same for other 
grades, the more varied the better, and the instrument 
will thus become a clinoineter, or grade-measurer. When 
it is placed upon any slope, and its sights directed to any 
object (such as a target on a rod, or a paper in a cleft 
stick) at the same height above the surface as its upper 
edge, that division on the brace which is cut by the plumb- 
line will indicate the inchnation of the slope. The A level 
described on page 94, may be used in a similar manner, a 
scale having been in the same way formed on the bar DE. 
An extempore clinometer may be made with a sheet of 
paper, a thread, and a pebble. Fig- 53. 

Take a sheet of paper of any 
shape, double it, and a straight 
line is formed; double it again 
along the straight line, and 
four right angles are obtained. 
Cut out one of the right an- 
gles, and double it so as to 
bring the sides of the right 
angle together, and it will be 
bisected, forming two angles of 
45°. Fold this in three equal parts, and angles of 15° 
will be formed ; repeat the last operations, and angles of 
5° will be obtained. The subdivision may be carried as 
far as desired. To use the instrument, form a plumb-line 
by tying a pebble to the end of a thread, and attach it at 
the centre of the angles. Holding the right angle to the 
eye, if the grade be descending, or the opposite corner if 
it be ascending, turn the paper till its edge is in the line 
which passes from the eye to some object at the same 




112 THE LOCATION OF ROADS. 

height above the surface. The plumb-hne will then mdi 
cate the angle of the slope. In the figure it strikes 5", 
equivalent, by the table on page 44, to 1 in 11. 

6. CALOULATIWa EXCAVATION AND EMBANKMENT 

The proper grade-line having been thus determined, 
and drawn on the profile, (which shows the heights of the 
ground over which the line passes) the difference between 
the height of the ground and that of the grade-line at any 
point, will of course represent the depth of cutting, (or ex- 
cavation) or the height of filling (or embankment) as the 
case may be, at that point. This depth, or height, in 
feet and decimal parts of a foot, should be written in red 
figures {cotes rouges) at the proper points of the profile. 
With these, knowing also the intended width of the road 
and the inclination of the side-slopes, the cubical contents 
of the excavations and embankments, or the amount of 
" earth-work," may be accurately calculated. 

The cost of the road will depend in a great degree 
upon the quantity of the " earth-work" to be done, and 
may be greatly lessened by making the amount of exca- 
vation precisely equal to that of embankment, so that 
what is dug out of the hills may just suffice to fill up the 
hollows. It is therefore very important for economy to 
calculate these amounts with accuracy before the final 
location of the line, so that if they are found to be unequal, 
the position and grades of the line may be changed to 
produce the equality desired. 

This accurate calculation is necessary, after the final 
location, for another reason ; inasmuch as the contractors, 
who usually perform the work, are paid, not by the day, 
nor in the lump, but by a certain price per cubic yard, the 



EXCAVATION AND EMBANKMENT. 113 

exact determination of the number of which is therefore 
required to ascertain their just dues. 

PRELIMINARY ARRANGEMENTS. 

« 

For calculating the cubical contents of the solid mass 
of earth cut out or filled in, four different methods are in 
common use. All four, however, require the same pre- 
liminary arrangements and preparations, which will there- 
fore be now given. 

Figure 54 is a plan (on a scale of 800 feet to the inch) 
and figure 55 a profile (on a vertical scale of 80 feet to 
the inch) of an old line of road, which it is desired to im- 
prove by cutting down the hill and filling up the hollow, 
so as to form a single slope, with a uniform grade, from 
A to B.* The distances between the stations are written 
horizontally ; the heights of the ground above the datum 
line are written along the vertical lines which represent 
them ; and at the extremities of these vertical lines are 
placed the numbers which represent the depths of cutting 
or filling at those points, and which are equal to the dif- 
ferences between the heights of the ground and of the 
"grade-line," or new road. 

SECTIO-PLANOGRAPHY. 

A method of representing the cuttings and fillings upon 
the plan, devised by Sir John Macneill, has been named 
*' Sectio-planography P Usually the plan and the profile 
are drawn separately, and when the former varies much 
from a straight line, it is difficult for an unpractised 



* Simms on Levelling, Am. edition, p. 81 

8 



EXCAVATION AND EMBANKMENT. 



115 



eye to discover the corresponding points 
of the plan and profile ; as the latter 
is formed by placing all the distances 
along a straight base line, and therefore 
fills a longer space than the winding plan ; 
and as the two are also frequently drawn 
far apart, or even on different sheets. 
In the improved method, the depths of 
cutting and of filling at each station are 
set off on one side or the other of the 
plan of the line, as laid down upon the 
map, so that all the information desired, 
with regard to any portion of the line, 
may be found on that very spot. The 
accompanying figure shows its applica- 
tion to the preceding example, the " plan" 
of which has been intentionally made 
very winding. 

To make the distinction more striking, 
the cuttings may be shaded with lines 
perpendicular to the line of the road, and 
the fillings with lines parallel to it ; or 
the former may be colored red, and the 
latter blue.* 



Fig. 56. 



TABULAR ENTRIES. 



The data of the profile, with those 
deduced therefrom, should be presented 
in a tabular form, such as that which fol- 
lows, and which refers to figure 55. 



* See Simms on Sectio-Planography. 



116 



THE LOCATION OF ROADS. 



1 


2 


3 


4 


5 


6 


7 

Fill. 


station. 


Distances. 


Heiglit of ground 
above datum line. 


Rise or fall 
of the grade line 
for each distance. 


Height of 

grade 

above datum. 


Cut. 

+ 


1 

2 
3 
4 
5 

6 

7 


561 
858 
825 
820 
825 
330 


46.0 
59.2 
53.9 
26.9 
0.9 
4.9 
10.0 


— 4.8 

— 7.3 

— 7.0 

— 7.0 

— 7.0 

— 2.9 


46.0 
41.2 
33.9 
26.9 
19.9 
12.9 
10.9 




18. 
20. 






19. 
8. 



4219 


36.0 



The ^r5^ column contains the number of the station, or 
point, the height of which above the datum Hne is con- 
tained in the third column. The second column records 
the distances between the stations. 

The fourth column shows the rise or fall of grade for 
each distance, obtained by a simple proportion, the whole 
distance and difference of height being known. Thus, 
4219: 561 : : 36 : 4.8. 

The ffth column shows the height of the grade line, 
i. e. of the road as improved, above the datum line at each 
station. The numbers in it are obtained by subtracting 
successively the fall between two stations, as recorded in 
the fourth column, from the height of the grade line at the 
preceding station. Thus, 46 —4.8 = 41.2. 

The sixth and seventh columns show the depths of cut- 
ting or filling at any station. They are the differences 
between the height (from column 3) of the ground at any 
station, and the height of the grade-line (from column 5) 
for the same station. 

The station (No. 4) at which the cutting ends, and the 
filling begins, is called a " Point of Passage." 



CUBICAL CONTENTS. 117 



CUBICAL CONTENTS. 



With these data the calculation may hs commenced, 
and the end areas — or middle areas, or both, according 
to the method adopted— be sought, and the cubical con- 
tents thence deduced. The details of these calculations 
are of great importance to the practical engineer, but oc- 
cupy so much space, that they have been transferred to 
the Appendix. The following are their results. 

" Averaging end areas" is the most usual method of 
calculation in this country, but gives a result which al- 
ways exceeds the correct amount, in a greater or less de 
gree, according to the inequality of the end areas. In the 
present example, its error in excess is 10,000 cubic yards, 
which amount, beyond what was justly due for the work 
done, would be paid by a company or town by which 
this improvement should be made, if their engineers 
should adopt this method of calculation. 

The calculation by " Middle areas'''' gives an amount 
which /a//^ short of the true one, by a deficiency equal to 
exactly half of the excess of the preceding method. 

" The Pris?noidal' formula" alone gives the correct 
amount ; which, in this example, is 2,200,968 cubic feet 
of excavation, and 1,541,152 of embankment. 

The fourth method, by " Mean Proportionals," gives 
a result always less than the true one, and exceedingly 
erroneous when one of the end areas is nothing. 

The substitution of the correct Prismoidal method for 
the erroneous ones which are so frequently employed, is 
demanded by every consideration of accuracy, economy, 
honesty, and'justice ; and the full calculations in the Ap- 
pendix show that the additional labor required is too tri- 
fling to be a reasonable obstacle. 



118 THE LOCATION OF ROADS 



BALANCING THE EXCAVATION AND EMBANKMENT. 

When the quantity of excavation on any given portion 
of the road exceeds that of the embankment, the excess 
is called " Surplus,''^ and must be deposited, upon the 
adjoining land, in masses called " Spoil-hanlis.^'' 

When the excavation is insufficient to make the em 
bankment, the deficiency is called '^ Wantage,''^ and must 
be supplied from extra " Side-cuttings''' in the neighbor 
ing fields. 

Both these cases are expensive and otherwise objection 
able ; it is therefore very desirable to make the excavation 
and embankment " balance" each other, so that the earth 
dug out may just suffice to fill up the hollows. If the 
calculations show much disparity in the two amounts, the 
location of the line must be changed in some way, so as 
to effect the desired equality. 

This equalization must, however, be restrained within 
certain limits ; for it should evidently be abandoned, when, 
in order to find sufficient excavation to make the embank- 
ment, it would be necessary to go to such a distance that 
the cost of transport would exceed the cost of making 
side-cuttings for the embankment, and of depositing the 
distant excavation in spoil-banks. The comparison ot 
the price of transport with that of excavation and of land, 
will therefore determine th.e distance within which- the 
balancing must be established. 

SHRINKAGE. 

The equality recommended must be taken with an im- 
portant qualification, dependent on the fact that earth 
transferred from excavation to embankment shrinks, or is 
compressed, so as to occupy, on the average, one-tenth 



SHRINKAGE. 119 

less space in bank than it did in its natural state, 100 cu- 
bic yards " shrinking" into 90. 

Rock, on the contrary, occupies more space when bro- 
ken, its bulk increasing by about one-half. 

In experiments made on a large scale, by Ellwood 
Morris, C. E.,* the shrinkage of light sandy earth was 
i of its volume in excavation ; of yellow clayey earth 
yV ; and of gravelly earth j\. The increase of hard 
sandstone rock, quarried in large fragments, was y\ of its 
volume in excavation ; and of blue slate-rock, broken into 
small fragments, /o. 

Upon some of the public works of the state of New 
York, the usual allowance has been for the shrinkage of 
gravel and sand 8 percent.; for clay 10 per cent.; for 
loam 12 per cent. ; for mucking, or surface soil, 15 per 
cent. ; and for clay " puddled" 25 per cent. The in- 
crease of bulk of rock was taken at one-third, or some- 
times at one-half; though some experiments showed that 
one yard of slate-rock made from 1.75 to 1,8 cubic yards 
of embankment. 

These considerations lead us to modify the require- 
ments of equality in the excavations and embankments, 
and to adjust them so that the former shall exceed the lat- 
ter by about 10 per cent. 

CHANGE OF GRADE. 

We will now take up the example on page 114, in 
which we find the excess of the excavation over the em- 
bankment, or its " surplus," (according to the correct cal- 
culation, of which the result is given, on page 117) to be 
659,816 cubic feet. We must therefore change the grade, 

* Journal of the Franklin Institute, October, 1841. 



120 THE LOCATION OF ROADS. 

SO as to lessen the excavation, and increase the embank- 
ment, till the former exceeds the latter by only one-tenth of 
itself. The grade line AB (figure 55) might be raised either 
at A or at B. The latter is preferable, since it will increase 
the gentleness of the slope. The height which it should 
be raised at B might be calculated in advance, but the 
complication of the resulting formula is so great, that it 
will be better to assume some height, (which an expe- 
rienced eye can do with considerable accuracy) and hav- 
ing found, by a simple proportion, the changes in the cut- 
tings and fillings at each station, to recalculate the whole 
cubic contents. If the desired difference has not been 
attained in the result, it will at least be a guide by which 
a second assumption can be made with a very close ap- 
proximation to precision. 

Consider the grade to be raised three feet at station 7. A 
proportion between the sum of the distances from station 1 to 
7, and that to any other station, will give the change of cutting 
or filling at that station. 



For station 2, 


4219 


: 561 : 


: 3 


: 0.4 


(C (( 


3, 


4219 


1419 : 


: 3 


1.0 


C< (( 


4, 


4219 


2244 : 


: 3 


1.6 


t( (( 


5, 


4219 


3064 : 


: 3 


2.2 


(( C( 


6, 


4219 


3889 : 


: 3 


2.8 



The place of station 4, i. e. the " Point of passage," ia 
changed by the elevation of the grade line AB, and removed 
towards station 3, to some new station 4' ; see Fig. 57. A 
problem here presents itself, to find the distance between the old 
and new points of passage, knowing the slope of the grade and 
that of the ground. Call the former m to 1, and the latter 
n to 1. Let the elevation of the new grade line above the old 
point of passage = h feet ; and the distance required = d. 

An inspection of the figure shows that the heights of the 
two right-angled triangles, whose bases are d, are respectively 



CHANGE OF GRADE. 



121 



Fiff. 57. 




d d d d 

— and — . It is also evident that - == }- A ; whence is ob- 

n m n m 

tained the general formula, 

mn 

d = h . 

m — n 

In the present case (see table on page 1 1 6) m 

825 



4219 
36-3 



128; 



128 X 31 
"-53.9-26.9 = ^^'=^"^^^^-^^ W^l = ^^- 

The new station 4' is therefore distant from station 3, 
825 — 65 = 760 feet, and from station 5, 820 + 65 = 885 feet. 

Adopting these new distances, and changing the cuttings and 
fillings in accordance with the elevations of grade obtained by 
the proportions on the preceding page, they will stand thus : 



Station. 


Distance. 


Elevation 
of grade. 


New Cut. 


New Fill. 


1 

2 
3 

4' 
5 
6 

7 


561 

858 
760 
885 
825 
330 


0.0 
0.4 
I.O 
1.6 
2.2 
2.8 
3.0 




17.6 
19.0 





21.2 
10.8 

3.0 



The calculations being repeated with these data, it will be 
found that the excavation will amount to 2,048,000 cubic feet, 



122 THE LOCATION OF ROADS. 

and the embankment to 1,980,000 ; an apparent surplus of 
68,000 cubic feet; but since, ia order to allow for the shrink- 
age, there should be an excess of 205,000, it appears that there 
is really a Wantage, and that the grade has been raised too 
much ; so that an elevation of only 2f feet at B would probably 
produce the desired balance. 

TRANSVERSE BALANCING. 

When the road lies along the side of a slope, so that it 
is partly in excavation and partly in embankment, it is ne 




cessary so to place its centre line, that these two parts of 
its cross-section may balance. When the ground has a 
uniform slope, the desired end would be obtained (if the 
side slopes were the same for excavation and embank- 
ment, and if no " shrinkage" existed) by locating the cen- 
tre line of the road on the surface of the ground. In other 
cases, as when the side of the excavation slopes 1 to 1, 
and that of the embankment 2 to 1 , a formula to determine 
the position of the centre line of the road may be readily 
estabhshed. 

If earth be wanted for a neighboring embankment, the 
amount of excavation may be easily increased by moving 
the road farther into the hill, with the additional advantage 
of lessening its liability to slip. The line may be thus 



TRANSVERSE BALANCING. 



123 



changed on the map, according to the notes of cross- 
sections in the level book, and be subsequently moved, by 
a corresponding quantity, on the ground. 

When the slope of the ground is very steep, the trans- 
verse balancing must be disregarded, and the road made 
chiefly in excavation, to avoid the insecurity of a high 
embankment, as vi^ill be explained under " Construction." 



DISTANCES OF TRANSPORT. 



The equality of the masses of excavation and embank- 
ment is not the only consideration. The distances to 
which it is necessary to transport the earth which is 
moved, must also be taken into the account. Suppose 
that a mass of earth, whose surface is ABCD, is to be 



B 



Fig. 59 






DC H G 

removed to the embankment whose surface is EFGH, and 
which has a thickness sufficient to make the two masses 
equal. The mean distance of the transport is required. 
Conceive the mass ABCD divided into a very great num- 
ber of smaller masses. The sum of the products of these 
portions, by the distance which each of them is actually 
moved, will equal the product of the sum of the portions 
{i. c. of the whole mass) by the mean distance. The 
mean distance therefore equals the above sum of products 
divided by the whole mass.* 

In such cases as usually occur on a road, in which the 

« Gayffier, p. 122. 



124 THE LOCATION OF ROADS. 

cubes of excavation and embankment are comprised be 
tween two parallel planes, whose horizontal traces are 
ABEF and DCHG, and in which sections made by other 
planes, parallel to the first, cut off equal partial volumes, we 
know, from the principles of mechanics, that the mean 
distance desired is equal to the distance of the centres of 
gravity of the two volumes. In the simple example above, 
the mean distance of transport would be the distance be- 
tween the centres of the two rectangles. 

The methods of apportioning the excavations among 
different embankments, which ought to be adopted in more 
complicated cases of various distances of transport, in 
order to attain the minimum of labor and expense, will be 
considered in the next chapter, which treats of actual 
" Construction." 

7. ESTIMATE OF THE COST OF A ROAD. 

A minute and careful estimate of every possible source 
of expense in the construction of a road, is a very impor- 
tant element in determining its location. The principal 
items are the Earthwork, Land, Mechanical structures. 
Engineering, and Contingencies. 

EARTHWORK. 

The amount of " Earthwork," or excavation and em- 
bankment, is supposed to have been determined by the 
preceding calculations. Its cost per cubic yard depends 
on the wages of labor, the quality of the earth, and the 
distance over which it is moved. 

Wages. The daily wages of an ordinary laboring man 
vary of course with the locality and the season, and range 
from 50 cents to Si. 25. In making the estimate, it mus 



ESTIMATE OF COST. 125 

not be overlooked, that if wages are at that time unusually 
low, they will be likely to rise, if the work be so large 
in amount as to make the demand for labor exceed the 
supply. 

Quality. The amount of labor required, for breaking 
up and removing any given volume of earth, will of course 
depend upon its degree of compactness and cohesiveness, 
which is termed its " quality T This is estimated by the 
proportion between the number of picks in use, and the 
number of shovels which these picks will keep constantly 
employed. Thus, if the earth be so loose that it can be 
shovelled up without being loosened by the pick, it is 
called "earth of one man." If it be so hard as to require 
one picker, or "getter," to be constantly employed, to keep 
one shoveller, or "filler," at v^^ork, it is called " earth of 
two men." If one " getter" can keep two " fillers" busy, it 
is " earth of 1^ men ;" its nomenclature being formed by 
dividing the total number of men employed by the number 
of volumes of earth removed. The "quality" of earth can 
be accurately determined only by actual experiment, though 
it may be estimated with tolerable precision by an expe- 
rienced eye. In deep cuts, borings should be made, or 
shafts sunk, to ascertain the nature of the lower strata. 
In this examination a knowledge of the geological ar- 
rangement of the district will be of great assistance. 

An average laborer can shovel into a cart, in a day of 
ten hours, from 10 to 14 cubic yards, measured in the 
embankment, of earth previously loosened with a pick or 
plough. Of hard and firm gravelly earth, or gravel and 
clay mixed, he can load 10 cubic yards ; of loam, (sand 
and clay) 12 cubic yards; and of sandy earth 14 cubic 
yards.* To loosen the earth will cost from 1 to 8 cents 

* Journal of Frankliu Institute, September, 1841. 



126 



THE LOCATION OF ROADS. 



per cubic yard ; the hardest earth requires to be picked ; 
the others may be ploughed ; and some sandy earth does 
not require any loosening, but may be shovelled up at 
once. At wages of one dollar per day, the cost of shov- 
elling into a cart would therefore be from 7 to 10 cents 
per cubic yard ; to which the cost of loosening must be 
added. If it were " earth of two men," it would cost 
double. The excavation of rock will cost from 50 cents 
to $1.00, according to its hardness, and the disposition of 
its seams. 

The following table shows the number of cubic yards 
which can be loosened, loaded, &c., by an average la- 
borer, in a day of 10 hours.* 



NATURE OP THE 
WORK. 


CHARACTER OF THE MATERIAL. 


Cnmrnon 
Earth. 


Loose and 
light earth. 


Mud. 


Clay and 
stony earth. 


Compact 
Gravel. 

7 
to 
11 


Rock, 

(blasted) 


Digging up, or 
Loosening. 


18 
to 
23 


16 




9 


2.4 


Excavation ; in- 
cluding throw- 
ing 6 to 12 feet. 


8 
to 
12 


8 


7 
to 
16 


4 




2.2 


Loading in bar- 
rows. 


22 




8 




19 




Transport by bar- 
rows; per hun- 
dred feet. 


20 
to 
33 








24 

to 

28 




Loading in carts. 


16 

to 

48 








17 

to 
27 


10 


Spreading and 
Levelling. 


44 
to 

88 




25 




30 
to 
80 





* Deduced from the experiments of M. Ancelin. 



ESTIMATE OF COST. 127 

The cost per cubic yard of each kind of labor will be 
readily obtained by dividing the days' wages by the num- 
ber of cubic yards in the table. 

The cost of throwing with the shovel is usually one- 
third of that of digging up. 

From 90 to 120 square yards of surface of embank- 
ment can be " trimmed" in a day. 

When the net cost of performing any work has been 
ascertained, one twentieth of it should be added for the 
cost of tools, superintendence, &c. ; and one tenth of the 
whole for the profits of the contractor. 

Distance. The third element in the price of earthwork 
IS the distance to which the excavations must be removed. 
If the road be on a side-hill, and be so located that the 
excavation from its upper side can be at once thrown over 
to make the embankment on its lower side, the cost will 
be little more than that of the simple excavation. But 
usually large amounts of earth require to be removed con- 
siderable distances, with great increase of expense. The 
methods to be employed will vary with the circumstances 
of the case, as will be explained under the head of " Con- 
struction." 

The comparative cost, per cubic yard, (according to 
experiments made at Fort Adams, Newport, R. I.) of ex- 
cavating earth, and removing it to various distances, with 
wheelbarrows, one-horse carts, and ox-carts, is given by 
the following table, which includes the cost of loosening, 
filling, and dropping ; and estimates a laborer's wages at 
$1.00 per day of 10 hours ; a horse, cart, and driver, at 
$1.34 per day of 9 hours; and an ox-team and driver 
$1.60 per day of 9 hours. The earth was ploughed up 
at a cost of | cent per cubic yard. 



128 



THE LOCATION OF ROADS. 





COST IN CENTS PER CUBIC YARD. 1 












Wheelbarrow. 


One-horse cart. 


Ox-cart. 


30 


5.5 


8.2 


8.6 


60 


6.9 


8.4 


8.8 


90 


8.2 


8.6 


89 


120 


9.5 


8.8 


9.1 


150 


10.9 


9.0 


9.3 


180 


12.2 


9.2 


9.4 


210 


13.5 


9.4 


9.6 


240 


14.8 


9.6 


9.8 


300 


17.5 


10.0 


10.1 


450 


24.2 


11.0 


10.9 


600 


30.8 


12.0 


11.8 


900 


44.1 


14.0 


13.4 


1200 


57.4 


16.0 


15.1 


1500 


70.7 


18.0 


16.8 



From the preceding table it appears, that, with its data, 
the cost, after loading, of renioving the earth 100 feet, 
was, in barrows, 4.43 cents per cubic yard ; in one-horse 
carts, .66 cent ; and in ox-carts, .56 cent. 

Some accurate experiments on the Birmingham and 
Gloucester Railway* make the cost in barrows, per 100 
feet, at ^1.00 per day, Vq" = '■^•^ cents ; the experiments 
of M. Ancelinf give y/ to y/ = 3 to 5 cents ; the Ameri- 
can translator of Sganzin| VV ~ ^i cents. 

It is usual in barrow-work, to consider any vertical 
transport of the earth as costing eighteen times as much 
as the same number of feet of horizontal distance ; though 
from accurate experiments it seems that the ratio should 
be as 24 to 1 for barrows, and as 14 to 1 for horse- 
carts. § 



* Laws of Excavation and Embankment on Railways, p. 13G. 
t See page 126. t Page 110. § Gayffier, p. 146. 



ESTIMATE OF COST. 129 

The cost of transport by any method will be expressed 

by the formula — 

P (2D + d) 

L X C ' 

in which P = price of day's work of the vehicle and its 
driver. 

D = mean distance of transport. 

d = distance which could have been gone over 
in the time consumed in each filling and 
emptying. 

L = the distance which would be gone over in 
a day by the vehicle, proceeding without 
interruption at its average pace ; usually 
between twenty and twenty-five miles, 
or between 100,000 and 130,000 feet. 

G = the cubic contents of the load, expressed 
in fractional parts of a cubic yard. 
If P = 1 34, D = 1 500, d = 1 000, L = 1 00,000, and C = |, 

the formula becomes Attttt^ ; — ^^•'^ cents.* 

100,000 X I 

The complete cost, with one-horse carts, of excavating 
earth, transporting it, and forming an embankment, is very 
completely expressed in a. formula enunciated in the Jour- 
nal of the Franklin Institute for September, 1841, by 
EUwood Morris, C. E. 

The average pace of a horse carting embankment is 
taken at 100 feet of trip, and back, per minute ; and the 
time lost in loading, dumping, &c., at four minutes per load. 

For the variable quantities the following symbols are 
employed : — 

a = number of feet in the average haul, or " lead," of 
the embankment. 

* For a table thus calculated, see Mailette, p. 91. 
9 



130 THE LOCATION OF ROADS. 

h — number of hours worked per day. 

c = daily wages of laborer, in cents. 

d= " " cart, including driver and all ex 

penses of carting. 
e = cost of loosening materials, in cents, per cubic 

yard ; ranging from one to eight, as stated on 

page 125. 
f = number of cart-loads required to form a cubic 

yard of bank. Usually 3 on a descending road; 

3|- on a level, and 4 on an ascending road. 
g = number of cubic yards which a medium laborer 

will load into a cart per day, ranging from ten 

to fourteen, as stated on page 125. 
Then the minutes in the day's work = 60 6 ; 

The minutes consumed in each trip = ; 

^ 100 

The number of trips, or loads hauled per day, is 

_ 606 

"-^+4' 
100 ^ ' 

The number of cubic yards hauled per day, is 

60& 



The cost of hauling, per cubic yard, is 

604 '^^{m+* 



/(ifo + O 



60& 



[A]. 



Adding to this the cost of excavation = — , that of 

§■ 
loosening = e, and that of trimming = 1 cent, we obtain, 
for the total cost of a cubic yard of embankment, 



ESTIMATE OF COST. 131 

^ -+1 [B]. 



g ' 60b 

Applying it to an actual case, in which a = 1000, 
6 = 10, c= 125, d = 175, e = 2\, f= Z\, g = 12, 
the formula [A] for the cost of hauling, becomes — 



60 X 10 



= 14.3 cents ; 



and the formula [B], for the total cost of a cubic yard of 

embankment, becomes — 

125 
2.5 + -— - + 14.3 + 1 = 28.2 cents. 

The actual cost, with these data, on an amount of 
22,000 yards, was 27.9 cents, differing from the calcula- 
tion only three-tenths of a cent ; and on a total amount of 
150,000 yards, the actual and calculated costs in no case 
differed more than one cent. 

An easy approximate rule for the average cost of haul- 
ing one cubic yard any distance on a level, with such 
carts and rates of travel as those above referred to, may- 
be deduced from formula A : — 

For 300 feet divide the wages of cart and driver by 24 
500 " " 'i 19 

1000 " " " 12 

1500 " « « g 

2000 " u it ^ 

2500 " " «' 6 

3000 " " " 5 

The greater the distance of the haul, the less is the 
proportional cost, in consequence of less time being lost 
in filling and dropping. 



132 THE LOCATION OF ilOADS. 

In excavation and embankment with the scraper or 

scoop, (the use of which will be explained under the head 

of Construction) the number of cubic yards moved per day 

of ten hours, a distance expressed by a feet (adding vertical 

4200 
height to horizontal distance) = — X~qqT-* If the wages of 

scraper and driver be denoted by c cents, and cost of loosen- 

cia -\- 931) 
in^ by d, the cost per cubic yard =d-\-—^ — tt-^- When 

o J i. J 4200 

a = 55, c = 275, and c? = 1, the cost becomes — • 

l+?Z5i55 + 93i)=,+ 9., = 10.7 cents. 
4200 

When an embankment is made of earth carried beyond 
a certain distance, (usually 100 feet in the direction of the 
length of the road) it is paid for twice ; once as excava- 
tion and once as embankment, according to prices previ- 
ously stipulated ; but when carried less than this distance, 
(as when thrown from the upper to the lower side of a road 
which is half in cutting and half in filling) only one price, 
that of the excavation, is estimated for ; and the amount 
of embankment in this situation must be subtracted from 
the total amount, before multiplying this by the embank- 
ment price. If a portion of an embankment is required 
to be made of some peculiar material, which can be ob- 
tained only from a greater distance than the other materials 
of the bank, a separate and higher price should be estima- 
ted for it. 

In our estimate, thus far, we have determined only the 
cost of the excavation and embankment. 

The land to be occupied by the road is another impor- 
tant item. The quantity to be taken having been calcu- 



ESTIMATE OF COST. 133 

lated, with due allowance for the extra width of the 
cuttings and fillings, is to be reduced to acres in agricul- 
tural districts, and to square feet in towns and villages. 
Its value, if not settled by agreement, must be determined 
by appraisers, who are, however, naturally too much in- 
chned to favor the interests of private individuals to the 
prejudice of the company, or public body, which con- 
stitutes the opposite party, subjecting them to the pay- 
ment of extravagant compensations. 

The cost oi fencing will vary with the locality. 

The mechanical structures, as bridges, culverts, &c, if 
numerous and large, add greatly to the cost of the road ; 
but, if important, must be confided to a professional engi- 
neer. 

The stonework is usually paid for by the cubic yard, 
but in some parts of the country by the "perch," of 25 
cubic feet.* Wood is paid for by the cubic foot, or 
" solid measure," when no one of its dimensions is as 
small as some conventional limit, which is usually 4 
inches ; but " board measure" (one-twelflh of the former) 
is employed when the wood is 4 inches, or less, in any of 
its dimensions. " Running measure," referring to length 
only, is used for simple constructions, which have small 
and regular cross-sections, as ditches, piles, &c. 

The Engineering expenses, including laying out, super- 
mtendence, ofSce-work, &c., are usually estimated at 10 
per cent, upon the amount of the other items. 

Every possible source of expense should be taken into 
the account, and an ample price for each alloWed ; but, 
finally, at least 10 per cent., upon the total amount, must 
be added for Contingencies. 

* More precisely 24| feet, its standard being a rubble wall, 16^ feet 
long, and 18 inches thick. 



134 THE LOCATION OF ROADS. 

Even then the actual expense will generally exceed the 
estimate.* For this opprobrium of the engineering pro- 
fession there are many causes. 

The price of labor, as the work proceeds, particularly 
if it be one of magnitude, may rise far above what it was 
at the time of the estimate. 

In a deep cutting, rock may be found, where earth was 
expected, and the cost of that part of the excavation will 
therefore be increased tenfold. 

Many improvements in the plan of the work are sug- 
gested and adopted as it proceeds ; almost always with an 
increase of cost. 

Finally, it must be confessed that many incidental ex- 
penses, trifling in themselves, but considerable in their 
aggregate, rarely fail to be overlooked in the original es- 
timate. 

8. FINAL LOCATION OP THE LINE. 

When the preceding operations of measuring, mapping, 
and calculating, have been performed upon each of the 
various lines of communication between the two extremi- 
ties of the route, which have been considered worth sur- 
veying, their relative merits are to be examined. One 
may be shorter ; another more level ; a third may require 
less earthwork, and so on. The good and bad points of 
each route are to be compared by the principles laid down 
on pages 68 and 69, and that one adopted which will en 
able the most labor to be performed on it with the least 

* On the twenty principal railroads in England, the average proportion 
of the actual cost to the original estimate was as 2| to 1. The least va- 
riation was 62 per cent excess ; in the greatest, the cost was nearly si? 
times the estimate. 



RECTIFICATION. 135 

number of horses, provided the expense of its construc- 
tion fall within the limits established by calculation, or by 
necessity.* The persons who are to make the selection 
and decision should have before them, 

1. A general map of the localities. 

2. A profile of each line. 

3. Cross-sections at short intervals. 

4. The calculations of excavation and embankment. 

5. Drawings of the bridges, culverts, &c. 

6. Specifications of all the works. 

7. Amounts of stone-work, timber, &c 

8. Analysis of the prices of each. 

9. Estimate of cost. 

10. Estimate of revenue. 

11. Descriptive memoir. 

The final location of the line adopted is then to be 
made. It consists chiefly in — 

1. Rectification of the straight portions of the line. 

2. Laying out its curves. 

3. Staking out its side-slopes. 

RECTIFICATION. 

The minor irregularities, bends, and zigzags of the line 
(caused in part by the transverse balancing) may often be 
removed by substituting for them one straight line, which 
will be the average of their deviations on either side. A 
flagstaff being placed at one end of the line, an observer, 
at the other end, by signals directs assistants to place " in 
line" the rods which they bear ; and the points thus found 
are marked by stakes, which are usually driven at every 
hundred feet. In the case of long lines, through a coun- 

* Parnell, pp. 322, 433. 



l'S6 THE LOCATION OF ROADS. 

try of forests, the use of the compass, or some other angu- 
lar instrument, is almost indispensable, for it is still an un- 
solved problem in engineering, how, without the aid of 
these, the Romans attained the wonderful straighlness 
with which they carried their roads over thickly-wooded 
hills and valleys, with such lofty disdain of the eifects of 

gravity. 

Fig. 60. 




When a hill rising between two points, as A and B, pre- 
vents one being seen from the other, two observers C and 
D may place themselves on the ridge, as nearly as possible 
in the line between the two points, and so that each can at 
once see the other and the point beyond. C looks to B, and 
by signals puts D " in line." D then looks to A, and puts 
C in line. C repeats his operation, and so they alter- 
nately " line" each other, continually approximating to the 
straight line between A and B, till they at last find them- 
selves both exactly in it. 

When a wood, or some such obstacle, intervenes between 
the two points, as in Fig. 61, a different method must be 
adopted. The direction from A to B not being exactly 
known, leaving a rod at A, set up another at C, as nearly in 
the desired line as possible. Go on as far as the two rods 
at A and C can be seen, and set up another at D, " in line" 
with A and C. Go on beyond D, and place another rod 



137 



I. SI. 



M^iSS^^ 



E, in line with D and C ; and so proceed, producing the 
straight Hne till it arrives at Z, opposite B. Measure the 
distance ZB, and move the stakes C, D, E, &c., towards 
the true line by a quantity proportional to their distances 
from A. Thus if AZ be 1000 feet, and ZB, the final 
divergence, be ten feet, a stake C, 200 feet from A, 
should be moved two feet to C, in order to bring it into 
the true hne AB ; and so, proportionally, with the rest. 



The angles, which are formed by the meeting of the 
straight lines established in the approximate location of 
the road, must be rounded by curves, to which the straight 
lines must be tangents at their points of junction. 

On every curve there is an unavoidable loss of poioer 
in the deflection of vehicles from the straight line which 
all bodies in motion tend to follow ; and there is dajiger 
from the effects of the centrifugal force. The resistance 
is inversely as the radius of the curve, i. e., greater as the 
radius of the cm've is smaller ; for the force required to 
draw a carriage around a curve may be considered as 
composed of two portions ; one equal to the force which 
would be required to draw it over a straight line of the 
same length as the curve, and the other dependent on the 
additional power necessary, at each instant, to draw it 
mto the curved line from the tangent in which it tends to 



138 



THE LOCATION OP ROADS. 



move. A certain amount of force being required to pro- 
duce the entire change in direction, the smaller the radius 
of a curve, the less space and time is given for the exer- 
cise of this force, and a larger share of it must therefore 
be exerted at each moment, with a great increase of labor 
and danger. 

It is therefore very important that every road-curve 
should have as great a radius as possible. It should 
never be less than one hundred feet. 

When a curve is necessary upon a steep grade, the in- 
clination should be flattened at that place in order to com- 
pensate for the additional resistance of the curve. On 
this account a zigzag line up a hill is more objectionable 
than an oblique ascent by a straight line. 

The curves which are employed to unite straight lines 
are usually either circular or parabolic arcs. 



CIRCULAR ARCS. 



Having given two 
straight hues meeting 
at C, (or which would 
so meet, if produced) 
it is required to mark 
out on the ground an 
arc of a circle to which 
these Hues shall be 
tangents. 

The simplest mode 
for an arc of small ra- 



Fig. 62. 
C 



U 



dius would be to find the centre, by erecting perpendicu 
lars to the tangent lines at equal distances, A and B, from 
their point of meeting C. The intersection, 0, of the 
perpendiculars would be the centre, from which the arc 



CURVES. 139 

might be swept with a cord of proper length. But 
curves are often employed with a radius of one or more 
miles, so that this method would seldom be practicable 
The curve must therefore be traced independently of its 
centre. 

In practice, instead of a circle, a polygon is marked 
out, with sides or chords each one hundred feet long. 
Stakes are set at the ends of each of these chords, and 
are therefore in the circumference of the desired circle. 
The chords themselves, in circles of large radius, will 
nearly coincide with the arcs. 

The question is now, in what manner to fix the position 
of these chords. Two methods are in common use ; one 
by " angles of deflection," and the other by " versed 
sines." The former is generally employed upon railroads, 
but requires the use of an angular instrument.* The 
latter dispenses with this, and is therefore the one which 
will be here explained. 




* For its details, see Col. Long, Mifflin, Vandegraaf, Traulwiue, tfcc. 



140 THE LOCATION OF ROADS 

The stations are supposed to be at equal distances 
(each of which is usually a chain of 100 feet) and the 
versed sine to be given, or to have been found by trial. 
Assume it at two feet, and let station 2 be the point at 
which the curve is to begin. From station 2 measure in- 
ward, towards the centre, half the versed sine (or one 
foot) to 2', and place there a rod. Stretch out the chain 
from 2, and bring its farther extremity into the line of 2' 
and the back station 1, and it will fix station 3, at which a 
stake is to be driven. From 3 measure inward the full 
versed sine to 3' ; draw on the chain till its extremity is in 
line with 3' and 2, and it fixes station 4. So proceed, 
measuring inward the full versed sine, at each station, till 
you arrive at the station (5, in the figure) where it is de- 
sired to end the curve, and to pass off on a tangent. 
There only half the versed sine is to be used. Station 6 

is thus found, and the line 5 6 gives the direction of the 

final tangent, as 2 1 gave that of the initial one. The 

stations 2, 3, 4, 5, thus found, will be points in the cir- 
cumference of a circle to which the lines 1 2 and 5 6 

are tangents. 

To find approximately intermediate points, measure 
outwards from the middle of each chord, a secondary 
versed sine = one fourth of the original versed sine. If 
more points are required, measure from the middle of the 
new chord, a tertiary versed sine = one fourth of the 
secondary one ; and so on. 

The versed sine has been thus far supposed to be 
known. To calculate it from the angle of two meeting 
lines, the following problems are required. 

Problem 1. To find the radius of the circular arc which 
unites two straight lines meeting at a given angle, the distance 



CIRCULAR ARCS. 



141 



ftom their intersection Fig. C4. 

to the initial and final 
points of the curve ,,V, 

being also given. 

In figure 64, ACB 
is the given angle, and 
A and B the initial 
and final points, at 
equal distances from 
the point of intersec- 
tion. The triangle 
CBO, right-angled at 
B, gives 

,^ tan. BCO X BC . 
60 = , t. 

rad. ^ 

The required radius is equal to the natural tangent (to radius 
unity) of half the given angle, Fig. G5. 

multiplied by the distance from 
the intersection to the beginning 
or ending of the curve.* 

Problem 2. To find the versed 
sine, having given the radius. 

Given the radius OA or OF, 
and any tvi'o equal chords, AE, 
and EF, required the versed 
sine ED. \ 

ED^ = AE^ — AD' 
AD= = AO^ — DO' = AO' — (EO — ED)^ — 
= A0= — (AO — ED)' = 
= A0» — AO' + SAO . ED — ED' = SAO . ED — ED'. 
.-. ED' = AE' — SAO . ED-f ED' 
SAO . ED = AE' 
AE' 
SAO ' 

i. e., the versed sine is equal to the square of the chord, di- 
vided by twice the radius. When AE := 100 feet, the versed 
sine is equal to 5000 feet divided by the number of feet in tag 




ED 



* AC and AB being known, Radius OA = 



AC X AH 
GH 



142 THE LOCATION OP ROADS. 

radius. When -^A.E — 66 ieet, the versed sine equals 2178 
feet divided by the radius. 

When the lines, which are to be united by a curve, do 
not actually meet, the angle which their directions form 
may be readily calculated ; but after a little practice it 
will be easier to assume some versed sine ; to run a trial 
curve with it ; and after ascertaining whether it be too 
arge or too small, to assume another nearer the proper 
one, and so proceed. 

Compound Curves. The above method supposes that 
the curve has the same radius, or degree of curvature, 
hroughout, and that it unites the two tangents at equal 
distances from their intersection. But it is often required 
to increase or to lessen the degree of curvature, and thus 
to form a " compound curve," as in the figure. To effect 
this, at the station where the change Fig. 66. 

is to be made, use, for measuring 
inward, half the sum of the old and 
new versed sine, and thence pro- 
ceed with the new one only. Thus, 
if 2 feet has been the original 
versed sine, and the features of 
the ground which is next to be \ / 
passed over require a curve of 6 '' 
feet versed sine to be employed, at the desired point use 
a versed sine of 4 feet, and thenceforward one of 6 feet. If 
the curvature is to be lessened, the same rule applies. 

Reversed Curves. It is sometimes necessary to reverse 
the direction of a curve, and to commence curving in a 
contrary manner, without allowing a straight line to in- 

* It is often desirable to know how far the curve will depart from the 
mtersectiun of ths taufjeut lines. In figure 64, the distance required 
= FC = OC — OF = V (OAH- AC'O — OA. 



PARABOLIC ARCS. 
Fig. 67 



143 



ervene. At one chain beyond the point at which it is 
desired to make the change, place a stake in the hne of 
the two last, and at it begin to use the proper versed sine 
in the contrary direction. 

PARABOLIC ARCS. 

The following method furnishes an easy means of ob- 
taining a Parabolic curve. 



Fig. 68. 




Divide the two tangent lines 1....13, and 13.... 12, (whether 
of equal or differejit lengths) into the same number of equal 
parts, as many as may be thought necessary. Number 
the points of division on one tangent with the odd num- 
bers 1, 3, 5, &c., up to the vertex ; and on the other tan- 
gent number them, from the vertex, with the even numbers 
2, 4, 6, &c. Join the points 1 and 2, 3 and 4, 5 and 6, 



144 THE LOCATION OF ROADS. 

and SO on ; and the inner intersections A, B, C, D, E, will 
be points in the curve desired. 

To fix the points of this curve upon the ground, tall 
stakes naust be placed at each of the points of division of 
one of the tangent lines, and two men be stationed on the 
other. One places himself at station 1, and directs his 
eyes to station 2. The other places himself at 3, and 
looks to 4. A third man, holding a rod, is moved, by al- 
ternate signals from each of the others, till he comes to a 
point which is in both their lines of sight at once. This 
will be the point A. The man at 1 now passes to 5, and 
looks to 6, the other remaining at 3. The rodman, being 
again placed in both their lines of sight, thus fixes the 
point B. The remaining points are similarly determined. 

The Parabolic curve, though little used in this country, 
is generally preferred in France, and has the following 
advantages over a circular arc. 

It approaches nearer to the intersection of the tangent 
lines ; and as they are supposed to have been originally 
placed on the most favorable ground, the less the curve 
deviates from them, the less increase of cutting and filling 
will it cause. The more numerous the divisions, the 
nearer does it approach the tangents. 

Its curvature is least at its beginning and its ending, so 
that its deviation from the straight line is less strongly 
marked. 

It can join two straight lines of unequal length, as in 
the figure ; while a circular arc, of constant radius, re- 
quires both the tangents to meet it at equal distances from 
their intersection. 



SETTING GRADE PEGS. 



145' 



SETTING GRADE PEGS. 



The line of the road having been marked out by the 
methods which have now been given, and stakes set at 
the end of every chain, small " level pegs" are then to be 
driven beside them, with their tops at the surface of the 
ground, and their heights above or below the intended 
height of the road (i. e. its " grade line") are to be ascer- 
tained by a levelling instrument, and the corresponding 
" Cut" or " Fill" marked upon the large stakes. 

Another form of the levelling field-book, better adapted 
for this work than that given on page 98, though less safe 
for beginners, is presented below. It refers to the same 
stations and levels, noted in the previous form of page 98, 
and shown in fig. 43. 



Sta. 


Dist. 


B. S. 


Ht. Inst, 
above 
Datum. 


F. S. 


Total 
Heights. 


A 










0.00 


B 


100 


2.00 


+2.00 


6.00 


—4.00 


C 


60 


3.00 


—1.00 


4.00 


—5.00 


D 


40 


2.00 


—3.00 


1.00 


—4.00 


E 


70 


6.00 


+2.00 


1.00 


+1.00 


F 


50 


2.00 
15.00 


+3.00 


6.00 
18.00 


—3.00 


—3.00 



In the above form it will be seen that a new column is 

introduced, containing the Height of the Instrument, (i. e. 

of its line of sight,) not above the ground where it stands, 

but above the Datum, or starting-point, of the levels. 

The former columns of " Ascent" and " Descent" are 

omitted. The above notes are taken thus. The height 

of the starting-point or " Datum," at A, is 0.00. The 

Instrument being set up and levelled, the rod is held at A. 

The Backsight upon it is 2.00 ; therefore the height of 

the Instrument is also 2.00. The rod is next held at B. 

10 



146* 



LOCATION OF ROADS. 



The Foresight to it is 6.00. That point is therefore 6.00 
below the instrument, or 2.00— 6.00= — 4.00 below the 
datum. The instrument is now moved, and again set 
up, and the backsight to B, being 3,00, the Ht. Inst, is 
-4.00+3.00= — 1.00, and so on : the Ht. Inst, being al- 
ways obtained by adding the backsight to the height of 
the peg on which the rod is held, and the height of the 
next peg being obtained by subtracting the foresight to 
the rod held on that peg, from the Ht. Inst. 

When the road is level, the " Cutting" or " Filhng" at 
any point is the height of that point above or below the 
level line. But when, as is generally the case, the road 
ascends or descends, farther calculation becomes neces- 
sary. The following is a form of Grade book, convenient 
for beginners. 



1 

Sta. 


2 

Dist 


3 


4 

Ht. Inst. 

above 

datum. 


5 


6 


7 


8 


9 


10 


11 


B. S. 


F.S. 


Ht. Peg 
above 
Datum. 


Rise or 
Fall of 
Grade. 


Ht.grade 
above 
Datum. 


Ht.Inst. 
above 
Grade. 


Cut. 


Fill. 



1 

2 
3 
4 


100 
100 
100 
100 


9.700 
1.800 

3.480 
1.798 


+9.700 
+7.900 
+8.280 
+6.908 


3.600 
3.100 
3.170 
9.873 

19.743 
16.778 

—2.965 


0.000 
+6.1.00 
+4.800 
+5.110 
—2.965 


+0.300 

+0.300 

Level. 

— 0.200 


+4.000 
+4.300 
+4.600 
+4.600 
+4.400 


5.400 
3.300 
3.680 
2.508 


1.800 
0.200 
0.510 


4.000 
7.365 


16.778 



The first six columns are similar to those of the form 
just given. The 7th column gives the rise or fall of the 
grade for each distance. The 8th is obtained by a con- 
tinual addition of the preceding. The 9th is the differ- 
ence of the 8th and the 4th, and is convenient for the 
subsequent " Staking out the side slopes." The 10th 
and 11th are the difference of the 6th and the 8th, as on 
page 116. 



STAKING OUT THE SIDE-SLOPES. 145 



STAKING OUT THE SIDE-SLOPES. 

The " line" which has been so often spoken of, is the 
centre-hne of the road — its axis — and the stakes which 
have now been set at every hundred feet, on both straight 
hnes and curves, have marked out only this centre line. 
Before the " Construction" of the road is commenced, 
other stakes must be set to show how far on each side of 
the centre line the cuttings and fillings will extend. The 
data required are the width of the road, the depth of the 
necessary cuttings or fillings, and the ratio of the side- 
slopes to unity. 

Assume that the road is to be 20 feet wide, the slopes 
2 to 1, and the cutting 6 feet. Add half the bottom width 
to twice the depth, and the sum, (10 + 2x6) = 22, is the 
" distance out" from the centre stakes, at which the cut- 
ting stakes must be set. They should be marked " 6.-1-," 
or " Cut 6," and be driven obliquely, so as to point in the 
direction of the slope. If the road had been in filling, the 
" distance out," would have been the same, but the stakes 
would have been marked " 6. — ," or " Fill 6." 

Staking out the side-slopes is thus seen to be very easy 
when the ground is level in its cross-section. But when 
it is side-long, farther calculations, or repeated trials with 
a levelling instrument, are required to find the " distance 
out" which will correspond to the height of the ground 
above or below the grade line at that precise distance 
out. 



A general formula for any case may be readily investigated. 
Examining first the up-hill side, and calling the slope of the 
ground m to 1 ; that of the side slopes nto\: the desired dis- 
tance from the bottom angle of the cutting, d ; and the height 



146 



THE LOCATION OF ROADS. 




of the ground above that bottom angle h ; we obtain, (as on 
page 121) 

— = rt + — : whence a :=n. • 

n m m — n 

20 
If A = 6, n = 2, and m = 10, i = 6 X -3- = 15. Then the 

o 

up-hill cutting stake will be 10 + 15 = 25 feet from the cen- 
tre stake. 

Examining next the down-hill side, and using a symmetrical 

^ -,, ^' y „ 7, '"'^ T 

notation, we have — ■=h — — , whence a =^ h .. — ; — . Let 
n m m -\- n 

20 
A' = 4, n = 2, and m = 10, 0!' = 4 X — = 6.7, and the " dis- 
tance out" of the down-hill stake will be 10 -\- 6.7 = 16.7 from 
centre. 

Cases of embankment will be represented by the above figure 
inverted. 



u^ 



THE CONSTRUCTION OF ROADS. 147 



CHAPTER III. 

THE CONSTRUCTION OF ROADS. 

" The torrent stops it not ; the rugged rock 
Opens, and lets it in ; and on it runs, 
Winning its easy way from clime to clime, 
Through glens lock'd up before." 

Rogers. 

CONTRACTS. ^ 

The actual " Construction" of a road, after its " Lo- 
cation" has been completed, may be carried on by days' 
work, under the superintendence of the agents of the com- 
pany, or town, by which it has been undertaken ; but it 
will be more economically executed by contract. A 
" Specification^'' is first to be prepared, containing an ex- 
act and minute description of the manner of executing 
the work in all its details. Copies of it, with maps, pro- 
files, and drawings of the proposed road, &c., are to be 
submitted to the inspection of the persons desiring to un- 
dertake it, who are to be invited by advertisement to hand 
in sealed tenders of the prices per cubic yard (or other 
unit of measurement) at which they will agree to perform 
the work. The proposals are opened on the appointed 
day, and the lowest are accepted, other things being equal. 
The " Contract,''^ which is to be then signed by the par- 
ties, should contain copious and stringent conditions as to 
the time and manner of performing the work ; stipulating 
when it is to be commenced, how rapidly to progress, in 
what order of parts, and when to be completed ; which 



148 THE CONSTRUCTION OF ROaDS. 

of the incidental expenses are to be borne by the con 
tractor, and for which he is to be remunerated ; in 
what cases material carried from excavation into em- 
bankment is to be paid for at the united prices of both ; 
what penalties for neglect are to be imposed ; when pay- 
ments for work done are to be made ; and so on ; always 
remembering that every thing must be expressed, and 
nothing left to be inferred.* 

The specification is considered to form jaart of the con- 
tract, and a " Bond" is appended, by which the contractor 
and his sureties are " holden and firmly bound" in a 
penal sum, " this bond to be null and void, if the said 
parties shall faithfully execute and fulfil the accompany- 
ing Contract." 

Each contract should include such a length of road, 
called " a section," (usually half a mile or a mile long) 
that materials for the embankments may be obtained from 
cuttings within its limits. There should be separate con- 
tracts for the mechanical structures required. The works 
which will need most time for their execution should be 
commenced first ; but no contract should be let, till the 
land which it includes is secured, or exorbitant demands 
will be made. 

It has been said that the lowest bid is usually accepted, 
but this 'is to be taken with great qualifications. The 

* In the contracts for the public works of the state of New York, one 
valuable paragraph comprehends every thing, saying, " To prevent all 
disputes, it is hereby agreed, that the engineer shall in all cases determine 
the amount or quantity of the several kinds of work which are to be paid 
for under this contract, and the amount of compensation at contract prices 
to be paid therefor ; and also that said engineer shall in all cases decide 
every question, which can or may arise, relating to the execution of this 
contract on the part of the said contractor, and his estimate and decision 
shall be final and conclusive." 



EARTHWORK. 149 

skill, competency, character, and responsibility of the 
contractor are as important as the lowness of his prices. 
A skilful and experienced contractor will often make a 
profit on a work, which another has abandoned after con- 
siderable loss. Bids, less than the actual cost of the 
work, are often made, both from ignorance and from kna- 
very. In the former case, if the proposals were accepted, 
the contractor would be ruined, and obliged to leave the 
work unfinished ; in the latter, he would hope to gain 
something by doing first the easy and profitable parts of 
the work, and then abandoning it. In both cases the 
remaining portions would be executed at greatly in- 
creased expense. Six contracts in England amounting to 
$3,000,000 being abandoned, were finished by the com- 
pany, and cost them $6,000,000. The engineer should 
therefore ascertain the lowest amount for which the work 
can be done, and not let it for less. 

The work done is usually paid for monthly, according 
to a measurement made by the inspecting engineer. Five 
or ten per cent is generally retained till the completion of 
the contract. 

The two main divisions of the operations necessary in 
the construction of a road, are its earthwork and its 
mechanical structures. 

1. EARTHWORK. 

The term earthwork is applied to all the operations in 
excavation and embankment, whatever the material. 

REMOVAL OF THE EARTH. 

The problem which is to be solved, both in theory and 
practice, is, " To remove every portion of earth from the 



150 THE CONSTRUCTION OF ROADS. 

excavation to the embankment by the shortest distance, in 
the shortest time, and at the least expense." 

It must also be deposited so as to form a consolidated 
mass, and so that not a particle of it will need to be again 
moved. 

The problem is very important in practice, for upon its 
mode of solution depends a large portion of the cost of 
the work ; and in theory, it requires the aid of the higher 
Calculus, since, to satisfy its conditions, the sum of the 
products, arising from multiplying all the elementary vol- 
umes of earth into the distances which they are carried, 
must be a minimum. 

We have seen, on page 123, that in the simplest case, 
that in which the whole of one excavation is to be carried 
into one embankment, we may use the product of the 
entire mass multiplied by the distance of the centres of 
gravity of its two positions. But when certain portions 
of a cutting are to be deposited in spoil-banks ; others to 
form part of an embankment, of which the remainder is 
to be obtained from side-cuttings ; &c., it does not appear 
a priori what arrangement would give a minimum ex- 
pense. In a few cases the proper course is evident ; as, 
if a hill is to be cut down, and its materials serve only to 
fill up a valley, and are in excess, the excavation from its 
summit is clearly the portion to be deposited in spoil- 
bank ; if the materials are insufficient to form the em- 
bankment, it is the part most distant from the hill which 
should be formed from a side-cutting ; if the excavation is 
to be carried in two different directions and is in excess, 
it is the part of the middle which should be rejected and 
deposited in spoil-bank. 

One general principle of transport may be readily de- 
duced. Let ABCD represent the plan of an excavation 



REMOVAL OF THE EARTH. 
Fig. 70. 

B E. 



151 



k--.^ 



% 



--l 



rru 



D C H G 

from which the embankment EFGH is to be formed. If 
the volume CDik, instead of being taken to GH/?w, should 
be transported to EFo?z, it follows that the embankment 
GHZm must be obtained from a portion of the excavation 
beyond the line ik, and that the paths of the two volumes 
will cross each other, which is therefore a disadvantageous 
disposition, since it increases the distances passed over. 
Any such crossing of the paths of the volumes trans- 
ferred, either horizontally or vertically, may be generally 
avoided by conceiving the solids of excavation and em- 
bankment to be intersected by parallel planes, such as 
DCHG, ik, Im, &c., and by transferring the partial solids 
in the manner indicated by the boundaries marked out by 
these planes. 

In many cases the most economical distribution of the earth, 
can be determined only by 
a special construction. 
Thus in the figure, sup- 
pose that earth is to be 
taken from A and B to 
form embankments at C 
and D ; it is required to 
know which should form 
the embankment at C, and 
which that at D, To bring 
the case within the ap- 
plication of the principle 



Fig. 71. 




152 THE CONSTRUCTION OF ROADS. 

just enunciated, conceive the triangle ABD to turn around the 
line AB as on a hinge, so that the point D comes to occupy a 
point D', symmetrical with its former position. 

It is now evident that to avoid the crossing of the paths, the 
earth from A must be taken to D', {i. e. D) and the earth from 
B to C ; AD' + BC being less than AC + BD'. If the point 
D' had fallen beyond C the reverse would have been proper. 
If the point D' had fallen within the triangle ABC, there would 
be no crossing in either mode of transport, but the proper one 
would be determined by a similar algebraic condition.* 

The choice would be indifferent, if 

BC — AC = BD — AD, 
orif AD — AC = BD — BC; 

for then, AD + BC = AC + BD. 

Two points, A and B, Fig. 72, being found which fulfil this 
condition, other points will be found at the intersection of arcs 

Fig. 72. 



C 

described from C and D as centres, with radii of which the dif- 
ferences are respectively equal to the given difference AD— AC, 
or BD — BC. If a great number of these points were found, 
the polygonal line ABEFG would become an hyperbola, pos- 
sessing the remarkable property of so dividing the transporta- 
tion, that C should receive all the excavation from one side of 
it, and D all from the other. 

Suppose that embankments at C and D, Fig. 73, are to be 
made from a mass of earth mnop, just equal to them in volume. 
The minimum of expense will be obtained by finding the curve 
AG, which shall divide the area rmiop into two parts equal to 



* Gayffier, p. 134. 



REMOVAL OF THE EARTH. 



153 




E D 

those required at C and D, and which shall also possess the 
properties enunciated in the preceding paragraph. If the line EF 
drawn perpendicular to CD, from its middle E, does not cut off 
a sufficient portion of the area to supply D, this shows that the 
curve will be concave towards C. Then divide geometrically 
the area mnop in the required proportion, by a straight line rs, 
inclined approximately as the curve would be, and adopt its 
middle point as a point of the curve. Then will BD — BC be 
the constant difference of radii required to find the other points 
of the dividing curve. 

If the amount of embankment, which might be deposited at 
C and at D, was indefinite, and the only requirement was its 
most economical removal from mnop, then the perpendicular EF 
drawn from the middle of CD, would divide the area into two 
portions, which should be removed to the points C and D re- 
spectively nearest to each of them. 

On similar principles may all such problems be resolved. 
Modifications of them are required, when the paths cannot be 
taken at will, as when a bridge, or an opening in a wall, is a 
point through which all the paths must pass. The number 
of bridges, of openings, of roads, &c., which will be most ad- 
vantageous, require separate investigations.* 



* See Gayfiier, pp. 137 to 142. 



154 THE CONSTRUCTION OF ROADS. 

EXCAVATION. 

The excavation and removal of earth is performed, ac- 
cording to circumstances, by ploughs, scrapers, barrows, 
carts, vv^agons, &c., each of vs^hich will be successively 
considered. 

LOOSENING. 

Most earth will require to be loosened with ploughs, 
spades, or picks, before being shovelled into the barrow, 
or cart, in which it is to be removed. The side-hill 
plough possesses some advantages. The picks should 
be two feet from point to point, not more than ten or 
twelve pounds in weight, and very deep and strong in the 
eye, or socket of the handle. Light and loose soil may, 
however, be at once taken up with the shovel. 

When the excavation is deep, the loosening may be fa- 
cilitated, with a great saving of time and labor, by digging 
a narrow channel to a depth of five or six feet, and under 
mining the face of the bank thus formed, letting it fall at 
once into the barrows, or carts, beneath it. Its disruption 
is hastened by wedges driven into its upper surface. The 
concussion of the fall breaks up the mass into small pieces, 
with great economy, but not without danger to the work- 
men. 

In the ordinary excavation, in which the earth is dug 
up, the united cohesion and weight must both be ovei- 
come ; in the method just described, the weight assists in 
overcoming the cohesion. Representing the force of co- 
hesion by 3, and that of the weight by 2 ; if both are to 
be overcome, as in the usual method, their resistance will 
be 3-1-2=5; while if the weight be made to assist the 
workman, the resistance will be only 3 — 2 = 1. 



EXCAVATION. 



155 



Steam has been applied to excavation, and a machine 
constructed, which can dig and load 1000 cubic yards per 
day, in favorable soil, at an annual cost, including inter- 
est, wear and tear, labor, &c., of $7,500, making the 

$7,500 
cost per cubic yard, ^^^ ^ ^^^^ = 2} cents.* 



SCRAPER OR SCOOP. 



This implement may be used with much advantage, 
when the earth yields readily to the plough, and is not to 
be moved more than 100 feet horizontally, nor to be 
raised to vertical heights of more than 15 feet; though 
these limits may sometimes be exceeded. The slopes of 
the banks which it forms, should not be steeper than li 
to 1. It usually contains j\ of a cubic yard.f The 

Fig. 74. 




ground, except when soft or sandy, requires to be previ- 
ously ploughed. The scraper is drawn by two horses, 
managed by a boy. The driver elevates the handles, and 
the iron-shod edge runs under the loose earth, rising up 

* Journal of the Franklin Institute, September, 1843. 
t Ibid. October, 1841. 



156 THE CONSTRUCTION OF ROADS. 

again as soon as the handles are released upon its being 
filled. It then runs with slight resistance upon two con- 
vex iron-shod runners, which project slightly beyond its 
bottom, and is thus drawn to the place of deposite. At 
that point the driver raises the handles ; its front edge 
catches in the earth, and its forward motion overturns it, 
and discharges its load. The horses keep moving ; and 
the scoop is dragged back to the place of excavation, in 
its inverted position, the handles resting on the tree. It 
is there loaded, &c., as before. 

BARROW-WHEELING. 

For excavations of moderate depths, and for distances 
within certain limits, harrows are most conveniently em- 
ployed. To facilitate emptying their contents, the bar- 
rows are made very shallow, with splaying sides, and with 
a very short axis to the wheel. They contain from o^ to 
yV of a cubic yard. They are wheeled on " runs" of 
plank, (as long and thick as possible) laid on the ground, 
or supported on trestles, or horses, numerous enough to 
prevent vibration. When the tracks are inclined, as in 
ascending from a deep excavation, they should be laid 
with a slope of one in twelve.* A steeper slope fatigues 
the workman excessively ; a flatter one increases- too 
much the length of his route. The same man does not 
usually dig, shovel, and wheel, but great advantages are 
obtained by a division of labor. One man picks, (if that 
be required) a second shovels into the barrow which stands 
on the edge of the excavation, and a third wheels the bar- 
row to the place of deposite, or to the next " stage," ac- 
cording to the distance. In the latter case, at the end of 



BARROW-WHEELING, 157 

the " stage," he meets another wheeler, returning with an 
empty barrow. The two there exchange their barrows ; 
the second man wheels on the loaded one over another 
stage, while the first man returns with the empty barrow 
to the excavation, where he finds a loaded one, which has 
been filled during his absence ; and so the circulation 
continues. 

The . length of the " stage" should be such, that the 
time, tali en by the wheeler to travel over it with a loaded 
barrov/, and to return with an empty one, should be just 
sufiicient to enable the shoveller to fill the barrow left at 
the excavation. It should vary therefore with the nature 
of the soil ; lessening, if this be easily worked, and in- 
creasing, if it offer greater resistance. On a level the 
length of a stage is usually from 60 to 100 feet. On an 
ascent of 1 in 12, it should be diminished by one-third ; 
on a similar descent it should be increased by the same ; 
for with this slope the labor on an ascent of 60 feet ex- 
actly equals a level stage of 90 feet.* 

If the distance were not divided into stages, and one 
man wheeled his barrow the entire length, a number of 
runs would require to be laid from the excavation. Such 
an arrangement would be inconvenient, from its blocking 
up the work, and expensive, from the cost of the plank. 
At the point where the run terminates in the excavation, 
two planks are placed, diverging like the letter Yj the 
full and the empty barrow being wheeled on each alter- 
nately. At the meeting of two stages, a double track is 
laid, to form a turning-out place for the exchange of the 
barrows. At the place of deposite, several planks should 
radiate from the main track, so that the earth may be at 

* Dupin. Applications de la Geometrie. 



158 THE CONSTRUCTION OF ROADS. 

once evenly distributed, by being emptied from each in 
turn, thus saving much subsequent levelling. 

Barrow-wheeling becomes too expensive after reaching 
a certain limiting distance of transportation. The frequent 
neglect of this consideration leads to much waste of labor. 
When earth is to be conveyed great distances, carts or 
wagons should be employed. The limit is determined 
by a combination of the cost of filling and of transporting. 
The table on page 128, makes it 100 feet; the limit in 
France, with barrows containing -^-^ of a cubic yard, should 
be 200 feet ; on English works, with barrows holding ^V 
of a cubic yard, the linait is 300 feet. The hmiting dis- 
tance becomes smaller as the height to which the earth 
is moved becomes greater.* 

CARTS, ETC. 

One-horse carts may be advantageously employed for 
distances exceeding the sphere of barrows. For short 
distances, the greater proportional loss of time in filling 
them more than balances their economy while moving. 
They should be made very light, and their box be bal- 
anced on a pivot, so that when loaded they will tend to 
discharge themselves.! As the distance increases, ivag- 
ons, drawn by two horses, become cheaper, and a tempo- 
rary railway may often be constructed with profit. 

When the length of the lead, (/. e. the distance from 
the face of an excavation to the head of an embankment) 
exceeds 1^ miles, and the amount of earthwork is con- 
siderable, a locomotive engine may be advantageously 
employed to draw trains of wagons upon the rails. 

* Gayffier, p. 159. 

+ When horses draw loads out of an excavation, the inclination of their 
track should not exceed 1 in 20. Dupin. Applications de la Giometrie 



CARTS, ETC. l59 

" Casting up hy stages'^ is a method sometimes em- 
ployed for removing the earth from deep excavations. A 
scaffold is prepared with a number of platforms, each five 
feet above the other, and each successive one receding, 
like the steps of a staircase. On each platform stands a 
man with a shovel. The laborer in the excavation throws 
the earth upon the first platform ; the man there stationed 
throws it up to the second ; and so on in succession till it 
reaches the surface. 

Hoj'se-runs are also resorted to in very deep excava- 
tions, where the banks are necessarily very high and steep. 
Upon the slope of the bank are placed two plank " runs," 
or tracks, reaching from the top to the bottom of the ex- 
cavation. The distance between them must be a little 
greater than the depth of the excavation. At the top of 
each is a pulley, over which plays a rope, the ends of 
which pass down the runs. Each end of the rope is 
fastened to the front of a barrow, and its length is so ad- 
justed that one barrow will be at the top of one run, while 
the other barrow is at the bottom of the other run. At 
the top of the excavation, a horse, attached to the rope, 
travels horizontally, alternately raising one barrow, which 
has been filled below, and lowering the other, which has 
been emptied at the top. A man has hold of each bar- 
row to guide it in its ascent and descent, the weights of 
the men balancing each other. This method is advan- 
tageous for depths exceeding 20 feet.* The use of bar- 
rows in such cases, with the proper inclinations for the 
runs, would require too great a distance to be travelled 
over. 

» Gauthey, ii. 197. 

11 



160 THE CONSTRUCTION OF ROADS. 



SPOIL-BANKS. 



The spoil-banks, formed by the deposites of the sur 
plus earth of an excavation, are usually shaped, as in the 



Fiff. 75. 




figure, with side-slopes of 1| to 1. If the land which 
they occupy be of little value, it will be economical to ex- 
tend them along the line AB, making them wider and 
lower within certain hmits ; since vertical transport costs 
so much more than horizontal.* The solution of the 
problem of minimum expense shows that for spoil-banks 
made with barrows, (slopes l^- to 1, and employing the 
customary ratio of 18 to 1, for the comparative expense 
of horizontal and vertical transport) the base AB should 
ho, fifteen times the height.! 

SIDE-SLOPES. 

To preserve the slopes of deep excavations from being 
gullied and washed down into the road, a ditch should be 
made along the upper edges of the cutting, in order to 
prevent the surface water of the neighboring land from 
reaching it. Upon the slopes themselves should be made 
ditches, called " Catch-water drains," running obliquely 
downwards, to receive the water of rams, and conduct it 
into the side ditches. 

The side-slopes may be advantageously sown with 
grass-seed. The roots of the grass wull bind the earth 

» See page 128. t Gayffier, p. 162. 



BLASTING. 161 

together, and prevent its slipping. A covering of 3 or 4 
inches of good soil should be previously spread over the 
side-slopes, but if they are steeper than If to 1, the soil 
will not lie upon them. They may also be sodded ; the 
sods being laid on, either with the grass side uppermost, 
or edgewise, with their faces at right angles to the slope. 
The latter, " Edge-sodding," is the most efficient, but 
most expensive. 

TUNNELING. 

When the excavation exceeds a certain depth, it will 
be cheaper to make a tunnel as a substitute. The amount 
of excavation will be much less, but the cost of each yard 
of it will be much greater. Calculation in each case 
can alone decide at what depth it would be economical to 
abandon the open excavation, and to commence the tun- 
nel. Sixty feet is an approximate limit in ordinary earth. 
The necessity for tunnels seldom occurs, however, in the 
construction of common roads, though frequent in the 
great roads of the Alps, and on railroads ; in the chapter 
devoted to which they will therefore be more fully noticed. 

BLASTING. 

Not only rock, but frozen earth, and sometimes very 
compact clay, are removed by blasting with powder. 
The holes are drilled by a long iron bar of the hardest 
steel, chisel-edged, which is raised and let fall on the de- 
sired point, and at each stroke turned partially around, so 
that the cuts cross each other like the rays of a star *. 
The holes are made from 1 to 3 inches in diameter, and 
from 1 to 4 feet deep. One man can drill in a day 18 
inches, of one 3 inches in diameter, in rock of average 
hardness. When water percolates into the hole, it must 



162 THE CONSTRUCTION OF ROADS. 

be dried with oakum and quicklime, and the powder en 
closed in a water-proof cartridge. The proper proportion 
of powder being introduced by a funnel and copper tube, 
(so that none may adhere to the side) a wadding, of hay, 
moss, or dry turf, is placed upon it, and the remainder of 
the hole is filled with some packing material. This is 
usually sand, but by far the best, for safety and efficiency, 
is dried clay, rolled into balls or cylinders, and dried at a 
smith's forge, as much as can be, without its falling to 
pieces. The next best material is the chippings and dust 
of broken brick, moistened slightly while being rammed. 
An inch or two of the wadding being simply pressed 
down upon the powder, the filling material is rammed, or 
" tamped," with a copper wire, till it becomes very com- 
pact. Through it passes, from the powder to the surface, 
some means of ignition. A straw, filled with priming 
powder, and ignited by a slow match, was formerly 
employed for this purpose. But of late years this has 
been generally, and should be universally, superseded by 
the safety-fuse. This has the appearance of a common 
tarred rope, and is so prepared that the length of it, which 
will burn any given time, can be exactly known, so that 
no premature explosion need be feared. 

The proper charge of powder, and the direction of the 
holes, are very important, both for efficiency and econo- 
my. The usual charge is one-third of the depth of the 
hole ; but such a rule is evidently irrational, for the 
amount of a charge so proportioned will vary with the 
bore. The proper regulator of the charge is the length 
of '^ the line of least resistance, '''' i. e. the shortest dis- 
tance from th(^ bulk of the powder to the outside of the 
rock. Thus in the figure, AB being the hole bored, and 
B the powder, BC is the " line of least resistance," 



BLASTING. 



163 



which should not be in the direction Fig. 76. 

of the hole bored. The proper charge 
depends on it, and not at all on the 
depth AB. To produce similar pro- 
portional results in different blasts, 
the charges must be as the cubes of 
the respective lines of least resist- 
ance. Thus, if four ounces of pow- 
der will just suffice to blast a solid rock in which BC is 
2 feet, the charge for another in which BC was 3 feet, 
would be given by the proportion 2^ : 4 : : 3^ : IS^ ounces. 
On these data the following table is formed.* 




Line of least 


Charges of 


Line of least 


Charges of 


resistance. 


powder. 


resistance. 


powder. 


Feet, inches. 


Lbs. Oz. 


Feet. Inches. 


Lbs. Oz. 


1 


Oi 


4 


2 


1 6 


1^ 


4 6 


2 131 


2 


4 


5 


3 14i 


2 6 


7| 


6 


6 12 


3 


13i^ 


7 


10 lU 


3 6 


1 5JL 


8 


16 



The following table will also be found very convenient 



Diameter of 


Powder in one 


Powder in one 


Depth of hole to contain. 


the hole. 


inch of hole. 


foot of hole. 


one lb. of powder. 


Inches. 


Lbs. Oz. 


Lbs. Oz. 


Inches. 


1 


0.419 


5.028 


38.197 


H 


0.942 


11.304 


16.976 


2 


1.676 


1 4.112 


9.549 


2| 


2.618 


1 15.416 


6.112 


3 


3.770 


2 13.240 


4.244 



* London Mechanics' Magazine, xxxiii. 597, Dec. 1840 ; and profes- 
sional papers of Royal Military Engineers, vol. 4. 



164 



THE CONSTRUCTION OF ROADS. 



When the rock is stratified, Fig. 77. 

having beds and seams, as in 
the figure, holes bored paral- 
lel to the joints will produce 
much greater effect than the 
usual vertical ones. 

When a rocky surface is to 
be cut down to a line AB, the holes should be oblique, as 

Fig. 78. 





in the figure. In some cases, a horizontal one, from B 
towards A would be advantageous. 

On a high face of rock a system of undermining may 
be usefully employed, by blowing out a mass below, and 
removing the remaining overhanging portion by crowbars, 
wedges, &c. 

The crater, or cavity formed by an explosion, is as- 
sumed to be a truncated cone, which has its inner or smaller 
diameter equal to half the diameter of the mouth of the 
crater. It has been found by experiment that the outer 
diameter of the crater may be increased, in ordinary soils, 
by excessive charges, to three times the length of the 
" line of least resistance," but not much beyond this ; and 
that within this limit this diameter increases nearly in the 
ratio of the square root of the charge. 

The most unfavorable situation for a charge is where a 
re-entering angle is to be blown out, as the rock all around 
it exerts a powerful resisting pressure. The charge needs 



EMBANKMENTS. 165 

to be proportionally increased. This case constantly oc- 
curs in blasting out narrow passages. 

No loud report should be heard, nor stones be thrown 
out. The best effect is produced when the report is 
trifling, but when the mass is lifted, and thoroughly frac- 
tured, without the projection of fragments. If the rock 
be only shaken by a blast, and not moved outwardly, a 
second charge in the same hole will be very effective. 

Any kind of compact brush, such as pine or cedar 
boughs, laid on rocks about to be blasted, will almost 
completely prevent the flying of fragments, and thus les- 
sen the danger to persons and buildings in the vicinity. 

The safety of blastuig operations may be greatly in- 
creased by applying galvanism to the ignition of the 
powder, which can then be effected at any distance. 
By its aid a row of blasts can be exploded simultaneously, 
by which their effective power is greatly increased. In 
this way, a single blast, of nine tons of powder, contained 
in three cells, removed one million tons of rock from a 
cliff at Dover, with a saving of $50,000 

EMBANKMENTS. 

Perfect sohdity is the great desideratum in aicificial 
road-making. Every precaution must therefore be em- 
ployed, in forming a high bank, to lessen its tendency to 
slip. From the space which the bank is to occupy, all 
vegetable or perishable matter, and all porous earth and 
loose stones, should be removed. On this space the 
earth is then deposited, to form the embankment, which 
is usually made of full height at its commencement, and 
is extended by " tipping" earth from the extremity, and 
so carried out on a level with the top surface. But an 
embankment thus formed will be deficient in compact- 



166 THE CONSTRUCTION OF ROADS. 

ness ; for the particles of earth, which are emptied from 
the top of the bank, will temporarily stop in their descent 
at the point of the slope at which the friction becomes 
sufficient to balance their gravity ; and when more earth 
comes upon them, they will give way and slide lower 
down, causing the portions above them to slip and crack, 
and thus delaying for a long time the complete consoli- 
dation. 

This method is, however, cheap and rapid. Its rapid- 
ity will be increased by obtaining more " tipping places," 
which can be effected by forming the bank at first wider 



Fig. 79. 




_-f? 



\ 



b B 

at top, and narrower at bottom, than it is finally to be, 
(i. e. forming ahcd instead of ABCD) and subsequently 
throwing down the superfluous earth from the top to give 
the proper width at bottom.* 

The solidity of embankments, which are made by 
tipphig from the ends may be increased by forming the 
outside portions of the bank first, and gradually filling up 
towards the middle, so that the earth may arrange itself 
with a tendency to move towards the centre, if at all.f 

To ensure the stability of embankments, they should, 
however, be formed by depositing the earth in successive 
layers or courses, not more than three or four feet thick ; 
and the vehicles, conveying the materials, should be re- 

* Laws of Excavation and Embankment on Railways, p. 59. 
t Mahan, p. 287. 



EMBANKMENTS. 



167 



quired to pass over the bank at each trip, so as to com- 
press the earth. If the case warranted the expense, each 
course might with advantage be well rammed. To les- 
sen the danger of slips, the layers should be made some- 
Fig. 80. 




W////////////M'^ 

what concave, as in Fig. 80. If made convex, as in the 
next figure, and as they are apt to become, in the most 

Fig. 81. 




w^w^mmmm^mmwmmm 



natural mode of forming them, portions would tend to 
slip off in the direction of the layers, while the arrange- 
ment of concave layers would resist, instead of assisting, 
any slip. A framework of timber has sometimes been 
inserted in a bank to bind it more firmly together. 

An embankment should always be formed at first of its 
full width, and not, from a mistaken economy, be at first 
made narrow, to be subsequently increased by lateral ad- 
ditions ; for the new portion will never unite perfectly 
with the old. 

At the foot, or " toe," of the bank, a slight excavation 
may be made to resist its tendency to spread, or a low 
but massive stone wall may be there erected. 

The slopes, like those of excavations, should be grassed, 
or sodded. If exposed to the action of water, a row 
of planks, grooved and tongued, and sharpened at bottom, 



168 THE CONSTRUCTION OF ROADS. 

should be driven at their foot, forming a "sheet-piling ;''* 
and the slopes themselves should be protected with a 
" slope-wall,'''' composed of rough stones, from one to two 
feel thick, laid without mortar, with their faces at right 
angles to the slope, and " breaking joints" as perfectly as 
possible. To prevent their being thrown out of place by 
the swelling and heaving, which is caused by the freezing 
of the rain-water retained by the clayey material of 
which an embankment may be composed, a layer, one or 
two feet thick, of coarse gravel, should be placed on the 
slope before laying the stone facing, so that the rain-wa- 
ter can at once pass through this porous coating. At the 
foot of the slope, an " apron," or mass of loose stones 
may be deposited. 

SWAMPS AND BOGS. 

When an embankment is to be made through a swamp, 
bog, marsh, or morass, many precautions are necessary. 

If the bog be less than four feet deep, and have a 
sohd bottom, all the soft matter should be removed, and 
an embankment raised upon the hard bottom. 

If it be deeper, but not very soft, the surface may be 
covered with two rows of swarded turf; the lower being 
laid with its grassy face downward, the other with that 
face upward, and the embankment raised upon them. 

When the swamp is deep and fluid, thorough draining 
is the first and most important point. On each side of 
the road, wide and deep ditches must be cut, to collect 
the surface water, and to carry it off into the natural wa- 
ter-courses. Numerous smaller ditches must be cut, at 
short intervals, across the road-way, from one main drain 
to the other, descending both ways from the centre. This 
operation will consolidate the surface between the main 



SIDE-HILL ROADS. 



169 



ditches. The cross-drains may be filled with broken 
stones, (or bushes, if they will always remain under wa- 
ter, as otherwise they will decay, and cause the road to 
sink) and on this foundation the embankment may be raised. 
In extreme cases, the lower portions of the embank- 
ment must be formed of brush-wood, arranged in fascines, 
which are a specific remedy against water. They are 
formed by carefully selecting the long, straight, and slen 
der branches of underwood, and tying them up in bundles, 
from 9 to 12 inches in diameter, and from 10 to 20 feet 
long. A layer of these fascines is laid across the road ; 
a second layer in the direction of the road ; and so on, to 
as great a thickness as may be required to raise the road- 
bed perfectly high and dry. Sharp stakes are driven at 
intervals to fasten together the layers. Poles, or young 
trees, may be laid across every other course. Upon this 
platform of fascines may be laid large flat stones, and upon 
them a course of earth and gravel. 



SIDE-HILL ROADS. 



When a road runs along the side of a hill, it will be 
most cheaply formed, by making it half in excavation and 
half in embankment. But as the embankment would be 




170 



THE CONSTRUCTION OF ROADS. 



liable to slip, if simply deposited on the natural surface of 
the ground, the latter should be notched into steps, or off- 
sets, in order to retain the earth. In adjusting the height 
of the made ground, an allowance should be made for its 
subsequent settling. 

If the surface be very much inclined, both the cuttings 
and fillings will need to be supported by "retaining walls," 



Fig. 83 




which may be laid dry if composed of large stones, or 
in mortar. The proper thickness which should be given 
to them, will be investigated under the head of " Me- 
chanical structures." 

If the side hill be of rock, the steep slope at which that 
material may safely be cut, will enable the upper wall to 
be dispensed with. 

When the road is required to pass along the face of a 
nearly perpendicular precipice, at a considerable height, 
(a case which sometimes occurs in passing a projecting 
point of the rocky bank of a river in a mountainous dis- 



TRIMMING AND SHAPING. 



171 



Fig. 84. 




trict) it may rest on a frame-work 
formed of horizontal beams, deep- 
ly let into the face of the preci- 
pice, and supported at their outer 
ends by oblique timbers, the low- 
er ends of which rest in notches 
formed in the rock. 

TRIMMING AND SHAPING. 



To form the side-slopes with 
precision, to the proper inclina- 
tion, a simple bevel, " 6aizr-level," 
or " clinometer," may be era- 
ployed with great advantage. It consists of two strips of 
baard, AB, AC, fastened to each other at right angles, 
and connected by a third Fig. 85. 

one, CB. When the de- 
sired slope is 2 to 1, make 
AB twice the length of AC. 
Place C, orB, at any known 
point of the slope ; make 
AC vertical by the plumb-hne ; and then will BC com- 
cide with the slope desired. 

Another implement for the same purpose is formed of 
a single strip of wood, to which is attached a triangle, 

Fig. 86. 





172 



THE CONSTRUCTION OF ROADS. 



with base and height corresponding to those of the de- 
sired slope. When a spirit-level, resting upon the top of 
this triangle, is horizontal, the inclined strip will coincide 
with the slope sought. 

A more general " Clinometer" is shown in the accom- 
panying figure. It consists of a spirit-level, moveable on 

Fig. 87. 




a pivot, which is the centre of a quadrant divided into de- 
grees. To measure a slope, place the bar upon it, and 
turn the level till the bubble is in its centre. The read- 
ing at the top of the level will indicate the inclination of 
the slope. To increase its portability, the long bar 
doubles up on a hinge in its middle.* 

To shape the tops of the embankments, and the bot- 
toms of the cuttings, in accordance with the desired pro- 
file of the road, attach, to the under side of a common 



* Simms on Levelling, p. 96. 



MECHANICAL STRUCTURES. 
Fiff. 88. 



173 




mason's level, a triangle ABC, with its base and height 
so proportioned as to correspond to the " crowning" of the 
road ; 1 in 24 for example. Or, instead of the triangle, 
gauges of different lengths, moveable on thumb-screws, 
maybe made to project below the level, to proper depths.* 

^. MECHANICAL STRITOTUEBS. 

Under this head are included the bridges, culverts, and 
other works of the mason and carpenter, which are re- 
quired for the purposes of the road. 



The most simple and natural form of a bridge consists 
of two timbers, laid across the stream, or opening, which is 
to be passed over, and covered with plank to form the 
road-way. Walls should be built to support each end of 
the timbers, and are named the abutments. The width 
of the opening which they cross is termed the stretch, or 
hay. The timbers themselves are the string -pieces. 
Their number and size must of course increase with the 
stretch. For a stretch of 16 feet, they should be about 

* Pamell, p. 261. 



174 



THE CONSTRUCTION OF ROADS. 



15 inches deep by 8 broad, and be placed at intervals of 
about 2 feet.* The greatest weight which can come upon 
them is when the surface of the bridge is covered with 
men standing side by side, and is then equal to 120 lbs, per 
square foot of surface, independently of the weight of the 
materials. Recent experiments make this only 70 lbs. 

This simple construction is only applicable to short 
stretches. For spaces of greater width, supports from 
the bottom of the opening may be placed at proper inter- 
vals. They may be piers of masonry, or upright props or 
shores of timber, properly braced, and supported on piles, 
if the foundation be insecure. They will divide the long 

Fig. 89. 




stretch into a number of shorter ones, and support the 
ends of the timbers by which each of them is spanned. 

But if the opening be deep, or occupied by a rapid 
stream, it is very desirable to avoid the use of any such 
obstructions. Means must therefore be devised for 
strengthening the beams, so as to enable them to span 
larger openings. This may be effected by supports from 
below, or from above. 

Of supports from below, the simplest are shorter tim- 
bers, (bolsters, or corbels) placed under the main ones, 

* Tredgold's Carpentry, p. 148. This gives a great surplus of strength. 



BRIDGES. 



175 



to which they are Fig- 90- 

firmly bohed, and \\ ] , 

projecting about '''^^'/'^/''WA 
one-third of the 
stretch. This will 
considerably in- 
crease the stiffness. 

Still more effective are oblique braces, or " struts," 
supporting the middle of the beam, and resting, at their 

Fig. 91 




lower ends, in " shoulders," cut into the abutments. Sim- 
ilar braces may be applied to the " bolsters" of Fig. 90. 
As the span increased, these braces would become so 

Y\g. 92. 




oblique as to lose much of their efficiency. A straimng- 
piece is therefore interposed between them. Thirty-five 
feet may thus be spanned. 

For longer stretches, the bolsters, braces, and straining- 
beams may be combined, as in Fig. 93. The principle of 

this method may be extended to very wide openings. 

12 



176 



THE CONSTRUCTION OF ROADS. 
Fig. 93. 




But in many cases supports from below may be objec 
tionable, as exerting too much thrust against the abut 
ments, and being liable to be carried away by freshets, 
&c. The beams must in such cases be strengthened by 
supports from above 

The simplest form of such is shown in Fig. 94, in 
which the horizontal beam is supported by an upright 

Fig. 94. 




" king-post," to which it is attached by an iron strap, 
as in the figure, or by the upright "king-post" being 
formed of two pieces, bolted together, and enclosing the 
beam between them. The king-post itself is supported 
by the oblique braces, or " struts," which rest against 
notches in the horizontal beam. 

Since the king-post acts as a suspending tie, an iron 



177 




rod may be advantageously substituted for it. The oblique 
braces may be also stiffened by iron ties, binding them to 
the main timbers, as in Fig. 95. 

For longer stretches, a straining beam may be intro- 

Fig. 96. 





duced between the struts, as in Fig. 96, in which the 
posts are represented as enclosing the beam. 

For bridges of greater span, and more complicated 
structure, the professional assistance of a civil engineer 
should be secured. The subject is therefore not carried 
any farther in this volume. For the same reason, bridges 
of stone and iron are omitted. A comprehensive analysis 
of them may be found in Professor Mahan's " Civil En- 
gineering." A recent work, "Haupt on Bridge Con- 
struction," (ISTew York, 1851) is an admirable treatise 
on the principles and practice of this important subject. 



178 



THE CONSTRUCTION OF ROADS. 



CULVERTS AND DRAINS. 

These structures are necessary for carrying under a 
road the streams which it intersects. They are also need- 
ed to carry the waters of the ditches, from the upper side 
of a road, to that side on which He the natural water- 
courses into which they must finally be discharged. Their 
simplest form consists of two walls of stone or brick, 
covered with slabs, and having a foundation, either of 
wood (if always wet) or of stone, laid in the form of an 
inverted arch, as shown in Fig. 97. 

cross-section in Figure 97. 
Their size must be propor- 
tioned to the greatest quantity 
of water which they can ever 
be required to pass, and should 
be at least 18 inches square, 
or large enough to admit a boy 
to enter to clean them out. Their bottoms should be in- 
clined 1 in 120, or 1 inch in 10 feet. When the road 
slopes, the inchnalion of the culvert may be increased, if 
necessary, by making it cross the road obliquely. At 
each end flat stones should be sunk vertically, or sheet- 
piling driven, to guard against the undermining effects of 
the water. The length of a culvert under an embank- 
ment will be equal to the width of the road, increased by 
the distance on each side, to which the slopes run out, at 
the depth at which the culvert is placed. At each end of 
it should be built wing-walls, their tops having an outward 
and downward slope corresponding to that of the embank- 
ment. Their ground plan may be rectangular, trapezoi- 
dal, or curved. 

In districts where stone is scarce, a small culvert may 




CULVERTS AND DRAINfe. 



179 



'^ 



13 



Fiff. 99. 




be constructed with four ranges of slabs -, Fig. 98. 

grooves being cut in the top and bottom [77 
slabs, to receive the upright ones which 
form the sides. 

A cheap culvert may be built of brick, 
with a semicircular arch, of three feet 
span, and 4 inches thick. 
One thousand bricks will 
build 26 running feet. If 
the flow of water be small, 
the bottom may be merely 
covered with gravel, over 
which is then poured grout of hydraulic cement, forming 
a superficial concrete. 

To obtain greater strength, the 
arch may rest on abutments, slo- 
ping inward, and the bottom of the 
culvert be a flat inverted arch. 

When a road is in excavation, 
the ditches on either side of it 
will sometimes require to be cov- 
ered, to prevent their being filled 
up by washings from the sides. 
They may then be formed as in 
Fig. 97 ; but spaces of half an inch in width should be 
left between the covering stones. A layer of brushwood 
should be placed over these, and the remainder of the 
ditch filled up to the surface Aviih broken stones, through 
which the water can filler.* 

vSimilar but smaller drains may be formed at intervals 
under the road, diverging from its centre like the two 




» Pamell, p. 95. 



180 THE CONSTRUCTION OF ROADS. 

branches of the letter Vj ^^<^ descending from the angu- 
lar point to the side-ditches. They are called " mitre 
drains." In very wet ground, a deep but narrow drain, 
filled with broken stones, may be carried through the 
middle of the road. 

CATCHWATERS, OR WATER-TABLES. 

These are very shallow paved ditches, formed across 
the road upon a slope, to catch the water which runs 
down its length, (and which would otherwise furrow up 
the road-way) and to turn it off into the side-ditches. 
They are also necessary in the hollows which exist at the 
points where a descent and ascent meet. They should 
be so laid that a carriage will not feel any shock in pass- 
ing over them. Their bottom may be flat, and six feet 
wide, and for twelve feet on each side they may rise one 
inch to the foot. The side-slope, down which they dis- 
charge their waters, should be also paved. Sometimes 
for economy they are used as a substitute for a culvert to 
carry the waters of a small stream across the road ; but 
this is very objectionable, particularly from the ledges of 
ice which will be there formed in winter. They are some- 
times shaped like a V? with the point directed up the as- 
cent, and will then divide the waters. In mountainous 
situations they should be located obliquely to the axis of 
the road, and the most advantageous position will evident- 
ly be that which has the greatest descent with the least 
length, and may be geometrically determined. 

Let the longitudinal slope of the road descending from A to 
B, be m to 1 ; and let its transverse slope from A to C be w to 
1 ; the former being here supposed steeper than the latter. 
It is required to determine the position of the catchwater AD, 
so that it may have the greatest slope possible. 



CATCH WATERS. 



181 



If a line, BC, be so drawn on the 
surface of the road as to be horizon- 
tal, the desired line of greatest slope, 
AD, will be perpendicular to it, as ex- 
plained on page 75. The position of 
this horizontal line must therefore be 
first determined. The two points, A 
and B, which it unites, being on the 
same level, the descent from A to B 
equals that from A to C. These de- 
scents are expressed respectively by 

AC . . , 

, givmg the equation. 



Fig. 101. 



and 




■ = : whence AC = AB • — . 

m n m 

Therefore, to obtain the position AD by a graphical con- 
struction, make AB of any length, and set off AC (as given by 
the equation) at right angles to it; join CB, and from A draw 
the perpendicular AD, which will be the line required. 

If it be required to define the position AD, by the angle 

BAD, it will be seen that BAD = ACB ; and that 

• .^T>_AB_ AB AB 

sm. AUB_ ^,j^ _ ^ ^^g, ^ ^^,^ 



V(AB« + AB^^) 



(l + £^)' 



V 



If m = 20 and n = 30, 
33° 45'. 



sin. ACB = .5555, and ACB = 



Care must be taken to avoid placing the catchwater in 
the direction of the diagonal of the rectangle formed by 
the four wheels of a carriage ; in order to avoid the double 
shock which would otherwise be caused by two wheels 
sinking into it at once. 

A cheap substitute for a catchwater on a steep slope is 
a mound of earth, crossing the road obliquely. This will 



182 



THE CONSTRUCTION OF ROADS. 



Fig. 102. 



also serve as a 
resting-place on 
the ascent. It 
should be so pro- 
portioned, that 
carriages may pass it without inconvenience. 




KETAINING WALLS. 



Retaining, sustaining, revetment, and breast walls, as 
their various names import, are employed to support 
masses of earth, and to resist their lateral pressure. Their 
use, when a road passes along a steep hill-side, has been 
already explained. In passing through villages also, where 
land is valuable, a narrower space will suffice for a road 
in excavation or embankment, if retaining walls be sub- 
stituted for side-slopes. 

The calculation of the necessary thickness for retain- 
ing walls, to enable them to resist the thrust of the earth 
which they are intended to support, is a problem of con- 
siderable intricacy of investigation, as well as one of much 
uncertainty, in consequence of the numerous and greatly 
varied data required. 



When a wall, of 
which ABCD is a 
transverse section, 
supports a mass of 
earth, there is a 
certain triangular 
portion, ADE, of 
the earth, which 
would slide down- 
ward if the wall 



Fig. 103. 




mmm^ 



were remioved, and which therefore now presses against 



RETAINING WALLS. 183 

tlie wall with a force, varying with its height, its specific 
gravity, and the angle, ADE, at which the earth would 
stand if unsupported. The wall may yield to its pressure 
by sliding along its base, or along some horizontal course, 
or by being overturned and revolving about the exterior 
edge of one of its horizontal joints. The latter is the 
only danger to be feared in a well-built wall. 

The most complete investigation of the problem of the proper 
thickness of retaining walls has been made by M. Poncelet in 
a Memoir,* of which a translation has appeared in the Journal 
of the Franklin Institute for 1843. It contains valuable ta- 
bles as well S.S formulcz. Let a denote the angle with the ver- 
tical made by the line of the natural slope of the earth, and 
represented by ADE in the figure. It will vary from 70°, as 
in the case of very fine dry sand, to 35°, as in the case of 
heavy clayey earth. Let w denote the weight of any unit of 
the earth, and lo' that of the same unit of the masonry. The 
specific gravity of the former ranges between 1.4 and 1.9, 

10 

and that of the latter between 1.7 and 2.5.+ The ratio — ; is 

w 

therefore usually between § and 1. For the simplest case, 

that in which the embankment does not rise above the wall, the 

formulaj for the thickness corresponding to any height H, is 



Tan. i-axAV^J^-H. 



This gives a stability of 1.92 to 1, or nearly double that of a 
strict equilibrium. 

For the usual assumed mean values of a = 45°, and 

w 

— = I, the formula gives for the required thickness of 

the wall yVo) 01' ^ Y\XX\q over a quarter of the height. 

* No. 13 du Memorial de Vofficier du Genie. See also Prony ; i?e- 
cherches sur la Poussee des Terres; and Navier ; Legons sur I'Appli 
tion de la Mecanique aux Constructions. 

+ Navier. t Poncelet, § 12. 



184 THE CONSTRUCTION OF ROADS. 

The extreme limits in any case are from j*oVo, or one- 
fifth of the height, with compact earth and heavy mason- 
ry, to T oVo5 or not quite half the height, with loose earth 
and light masonry.* The precise thickness can be cal- 
culated by the preceding formula ; after noting the slope 
at which the earth naturally stands, and weighing a cer- 
taui portion of the masonry, and of the earth previously 
thoroughly moistened. 

When there is an embankment rising above the top of 
the wall, the proper thickness (in cases in which the height 
of the superincumbent load does not much exceed the 
height of the wall) may be approximately obtained by 
substituting in the same formula, instead of the height 
of the wall, the sum of the heights of the wall and of the 
earth above it.f 

Thus far both faces of the retaining wall have been 
supposed to be vertical. But the same strength with a 
less amount of material may be ob- Fig. 104. 

tained by various modifications of its %>, 
section. 

The face of the wall may be advan- 
tageously made to slope with a " hatir^'' 
varying from 2V ? or \ inch horizontal 
to 1 foot vertical, to |, or 2 inches to 1 
foot. 




W0 



To find the mean thickness of such a 
wall, which shall have the same stability 
as another wall with vertical faces, and 
of the thickness obtained by the preceding rules, subtract from 
this given thickness four-tenths of the entire projection of the 
hatir-X Thus, if the given thickness be 4 feet, and the height 
24 feet, and the corresponding mean thickness of a wall with 

* Poncelet, § 34. t Ibid. § 22. \ Ibid. § 72. 



RETAINING WALLS. 



185 



&bdtirofj\ be desired, it will be 4 . — y'VXt|=4 . — .8=::3.2. 
The bdtir is supposed not to exceed one-fifth of the height. 
From the mean thickness, those of the top and bottom are 
readily deduced, knowing the height and bdtir. 

Fig. 105. 



The desired increase of thick- 
ness towards the bottom of a wall 
IS often given by offsets at its 
back. Considerable resistance to 
the overturning of the wall is of- 
fered by the weight of the earth 
which rests upon these offsets. 



Still more economical of 
masonry is a leaning retain- 
ing wall, in which the back 
has a bdtir, which may ad- 
vantageously be 1 in 6. In 
this case strength requires 
that the perpendicular let fall 
from the centre of gravity 
of the section upon the base, 
should fall so far within the 
inner edge of the base, that 
the stone of the bottom course of the foundation may 
present sufficient surface to bear the pressure upon it.* 




* Mahan, p. 142. 



1S6 THE CONSTRUCTION OF ROADS. 

The strength of a wall may be still farther increased by- 
lessening its thickness, and employing the difference of 
the amount of masonry in buttresses or counter-forts, at- 
tached to its back at regular intervals, and firmly banded 

Fig. 107. 




with it. The trapezoidal section for them is preferred, as 
giving a broader base of union. Fig. 107 is a ground plan 
of such an arrangement. 

To lessen the pressure of an embankment, that portion 
of it next the wall should be formed in compact layers, 
inclining downward from the wall. Through the wall 
should be left holes (barbacanes) six inches high and three 
wide, disposed, in the quincunx form, at distances of six 
feet horizontally, and four feet vertically, in order to give 
vent to the water which may filtrate through the bank. 

The masonry of a wall which has to sustain great 
pressures, requires much attention. The following is 
part of the specification for such walls of rubble ma- 
sonry on the public works of the state of New York. 
" The stone shall be sound, well-shaped, and durable, 
and of not less than 6 inches in thickness, and three feet 
area of bed. The smoothest and broadest bed shall in 
all cases be laid down, and if it be rough and uneven, all 
projecting points shall be hammered off; and the same 
from the top bed, so as to give the succeeding stone a 
firm bearing. In all cases the bed shall be properly pre- 
pared, by levelhng up, before the next stone is laid, but 



RETAINING WALLS. 187 

no levellers shall be placed under a slone by raising it 
from its bed. One-fourth of the wall shall be composed 
of headers, which shall extend through the wall, where 
it is not more than two feet thick, and from 2 to 4 feet 
back for thicker walls. The whole shall be laid in hy- 
draulic mortar, composed of the best quality of cement, 
and clean sharp sand ; and particular care shall be taken 
to have each stone surrounded with mortar, and tho- 
rouffhlv bedded in it." 



188 IMPROVEMENT OF THE SURFACE. 



CHAPTER IV. 

IMPROVEMENT OF THE SURFACE. 

" Next to the general influence of the seasons, there is perhaps no cir- 
cumstance more interesting to men in a civilized state, than the perfection 
of the means of interior communication." 

Committee of House of Commons, 1819. 

The surface of a newly-made road is generally very 
deficient in the important qualities of hardness and smooth- 
ness, and to secure these attributes in their highest at- 
tainable degree, it is necessary to cover the earth, which 
forms the natural surface of the road, with some other 
material, such as stone, wood, &c. The benefits of such 
a process are twofold, consisting, 

1. In substituting a hard and smooth surface for the 
soft and uneven earth ; 

2. In protecting the ground beneath it from the action 
of the rain-water, which, by penetrating to it, and remain- 
ing upon it, would not only impede the progress of vehi- 
cles, but render the road too weak to bear their weight. 

Such a covering should be regarded, not as an arch to 
bear the weight of the vehicles, but simply as a roof, to 
protect the earth beneath it from the weather ; not as a 
substitute for the soil under it, but only as a protection to 
that soil to enable it to retain its natural strength. Erro- 
neous views on this point have caused very prejudicial 
practices, particularly in the case of broken stone, or 
McAdam-roads. 



EARTH ROADS. 189 

The various surfaces will be considered in the following 
order ; beginning with the most imperfect, that of the 
unimproved earth, and ending with the most perfect yet 
attained — that of Railroads. 

1. EARTH ROADS. 

2. GRAVEL ROADS. 

3. BROKEN STONE, OR McADAM ROADS. 

4. PAVED ROADS. 

5. ROADS OF WOOD. 

6. ROADS OF OTHER MATERIALS. 

7. ROADS WITH TRACKWAYS. 



1. EARTH ROADS. 

Roads of earth, with the surfaces of the excavations 
and embankment unimproved by art, are very deficient at 
all times in the important requisites of smoothness and 
hardness, and in the spring are almost impassable. But 
with all their faults, they are almost the only roads in this 
country, (the scantiness of labor and capital as yet pre- 
venting the adoption of better ones) and therefore no pains 
should be spared to render them as good as their nature 
will permit. 

The faults of surface being so great, it is especially ne- 
cessary to lessen all other defects, and to make the road in 
all other respects as nearly as possible " what it ought to 
be." Its grades should therefore be made, if possible, as 
easy as 1 in 30,* by winding around the hills, or by cut- 
ting them down and filling up the valleys. Its shape 
should be properly formed with a slope of 1 in 20t each 

* See page 41. t Page 51. 



190 IMPROVEMENT OF THE SURFACE. 

way from the centre. Its drainage should be made very 
thorough, by deep and capacious ditches, sloping not less 
than 1 in 125,* in accordance with the minimum road 
slope. Drainage alone will often change a bad road to a 
good one, and without it no permanent improvement can 
be effected. Trees should be removed from the borders of 
the road, as intercepting the sun and wind from its surface. 

If the soil be a loose sand, a coating of six inches of 
clay carted upon it, will be the most effective and the 
cheapest way of improving it, if the clay can be obtained 
within a moderate distance. Only one-half the width 
need be covered with the clay, thus forming a road for the 
summer travel, leaving the other sandy portion untouched, 
to serve for the travel in the rainy season. 

If the soil be an adhesive clay, the application of sand 
in a similar manner will produce equally beneficial results. 
On a steep hill these improvements will be particularly 
valuable. 

When the road is worn down into hollows, and requires 
a supply of new material, its selection should be made 
with great care, so that it may be as gravelly as possible, 
and entirely free from vegetable earth, muck, or mould. 
No sod or turf should ever be allowed to come upon the 
road, to fill a hole or rut, or in any other way ; for, though 
at first deceptively tough, they soon decay, and form the 
softest mud. Nor should the roadmaker run into the other 
extreme, and fill up the ruts and holes with stones, which 
will not wear uniformly with the rest of the road, but will 
produce hard bumps and ridges. The plough and the 
scraper should never be used in repairing a road. Their 
work is large in quantity, but very bad in quality. The 

* See page 54. 



EARTH ROADS, 191 

plough breaks up the compact surface, which time and 
travel had made tolerable ; and the scraper drags upon 
the road from the side ditches the soft and alluvial matter 
which the rains had removed, but which this implement 
obstinately returns to the road. 

A very good substitute for the scraper, in levelling the 
surface of the road, clearing it of stones, and filling up 
the ruts, consists of a stick of timber, shod with iron, and 
attached to its tongue or neap obliquely, so that it is drawn 
over the road " quartering," and throws all obstructions 
to one side. The stick may be six feet long, a foot wide, 
and six inches thick, and have secured to its front side a 
bar of iron descending half an inch below the wood. 

Every hole or rut in a road should be at once filled up 
with good materials, for the wheels fall into them like 
hammers, deepening them at each stroke, and thus in- 
creasing the destructive etfect of the next wheel. 

EFFECT OF WHEELS ON THE SURFACE. 

The effects of broad and narrow wheels upon roads 
have been much discussed, and many laws enacted to 
encourage the use of the former. Upon a hard and well- 
made road, (such as one of broken stone) there is little 
difference between them, but on a common earth road, 
narrow wheels, supporting heavy weights, exercise a very 
destructive cutting and ploughing action. This dimin- 
ishes as the width of the felloe increases, which it may 
do to such an extent, that the wheel acts as a roller in im- 
proving, instead of injuring, the surface. For these rea- 
sons the New York turnpike law enacts that carriages, 
having wheels of which the tire or track is six inches 
wide, shall pay only half the usual tolls ; those with 

wheels nine inches wide, only one-fourth ; and that those 

13 



192 IMPROVEMENT OF THE SURFACE. 

with twelve inches shall pay none at all. The proportions 
agree precisely with those deduced from observation by 
an experienced English roadmaker.* The felloe should 
have a flat bearing surface and not a rounded one. The 
benefits of broad wheels are sometimes destroyed by over- 
loading them. To prevent this, when tolls are collected, 
they should be increased, for each additional horse, more 
rapidly than the direct proportion ; thus, if one horse paid 
5 cents, two should pay 1 1, three 17, &c. Narrow wheels 
are particularly injurious when in rapid motion, for having 
less resistance and greater velocity than others, they re- 
volve less perfectly, and drag more, thus producing the 
worst sort of effect. Conical wheels, of which the inner 
is greater than the outer circumference, tend to move in 
a curve, and being forced to proceed in a right line, exert 
a peculiarly destructive grinding action on the road. On 
McAdam roads, horses' feet exercise a more destructive 
effect than the wheels of vehicles. It has been calcula- 
ted! that a set of tires would run 2700 miles in average 
weather, but that a set of horses' shoes would bear only 
200 miles of travel.J 

* Penfold, p. 22. t Gordon on Locomotion. 

X The imperfect surface of an earth road makes it doubly important 
to take every precaution to lessen the friction of vehicles upon it. The 
resistance decreases as the breadth of the tire increases, on compressible 
roads, as earth, sand, gravel, &c. ; while on paved and broken-stone roads, 
the resistance is nearly independent of the breadth of the tire.* Cylin- 
drical vi^heels also cause less friction than conical ones. The larger the 
wheels the less friction have they, and the greater power of leverage in 
overcoming obstacles. The fore-wheels should be as large as the hind ones, 
were it not for convenience of turning. The axles should be straight, 
and not bent downward at the end, which increases the friction, though 
it has the advantage of throwing the mud away from the carriage. The 
load should be placed on the hind wheels rather than on the fore ones 
* Morin, p. 339. 





GRAVEL ROADS. 193 



2. GRAVEL ROADS,* 

The roundness of the pebbles, which form the chief 
part of gravel, whether from rivers or pits, prevents them 
from perfectly consolidating, except under much travel ; 
but still a gravel road, properly made, is far superior to 
one of common earth. Gravel from the shores of rivers 
is too clean for this object, and does not contain enough 
earthy matter to unite and bind together its pebbles, which 
are too perfectly water- worn, and freed from asperities. 
On the other hand, gravel dug from the earth contains too 
much earth, which must be sifted from it before use. Two 
sieves should be provided, through which the gravel is to 
be thrown. One should have wires, an inch and a half 
or two inches apart, so that all pebbles above that size 
may be rejected. The other should have spaces of three 
quarters of an inch, and the material which passes through 
it should be thrown away, or employed for foot-paths. 
The expense of sifting will be more than repaid by the 
superior condition of the road formed by the purified ma- 
terial, and the diminution of labor in keeping it in order. 

The road-bed should be well shaped and drained. If 
it is rock, all projecting points should be broken off, and 
a layer of earth, a foot thick, should be interposed, or the 
gravel will wear away much more rapidly, and consoli- 
date much more slowly. 

Long and pliant springs greatly lessen the shock of passing over obsta- 
cles, and their advantage has been stated to be equal to one horse in four 
The line of draught should ascend at an angle of 15 degrees, so that 
when the horse leans forward in pulling, his force will be exerted nearly 
horizontally. 
* Parnell, p. 170. Penfold, p, 13, Amer. Railroad Journal, vol. ii. p. 4. 



194 IMPROVEMENT OF THE SURFACE. 

A coating oi four inches of gravel should be spread 
over the road-bed, and vehicles allowed to pass over it 
till it becomes tolerably firm, and is nearly, but not en- 
tirely, consolidated ; men being stationed to continually 
rake in the ruts, as fast as they appear. A second coat- 
ing of 3 or 4 inches should then be added and treated like 
the first ; and finally a third coating. A very heavy roller 
drawn over the road will hasten its consolidation. Wet 
weather is the most favorable time for adding new ma- 
terials, 

A very erroneous practice is that of putting the larger 
gravel at the bottom, and the smaller at the surface ; for, 
from the effects of the frost, and of the vibration of car- 
riages, the larger stones will rise to the surface and the 
smaller ones descend, like the materials in a shaken sieve, 
and the road will never become firm and smooth. 

3. BKOKEN-STONE ROADS. 

Broken-stone roads have been the subjects of violent 
partisanship on many disputed points, and the most im- 
portant of these questions relates to the propriety or ne- 
cessity of a paved foundation beneath the coating of bro- 
ken stones. McAdam warmly denies the advantages of 
this, while Telford supports and practises it. Broken- 
stone roads may therefore be conveniently divided into 
McAdam roads and Telford roads. 

McaDam roads. 

Mr. McAdam, who first brought into general use in 
England roads of broken stone, and from whom they de- 
rive their popular name, is said* to have deduced the 

* Millinjrton, p. 234. 



McADAM ROADS. 195 

leading principles of his improved system from his obser- 
vation of the passage of a heavy vehicle, such as a loaded 
stage-coach, over a newly-formed gravel road. The wheels 
sink in to a considerable depth, and plough up the road, 
in consequence of the roundness of the pebbles, which 
renders them easily displaced. Hence ensues great fric- 
tion against the wheels ; which, moreover, are always in 
hollows with little hills of pebbles in front of them, which 
they must roll over or push aside. The evil continues, 
until at last, after long-repeated passages of heavy vehi- 
cles, the pebbles have become broken into angular frag- 
ments, which finally form a compact mass. 

But since this is so desirable a consummation, the task 
of breaking the stones ought not to be imposed on the 
carriages, but should be performed in advance by manual 
labor, by which it will be executed far more speedily, 
effectually, and completely. 

Hence is deduced the leading pnnciple of the system, 
viz. : that the stones should he all h'ohen hy hand i?ito 
angular fragjnents before being placed on the road, and 
that no rounded stones should ever be introduced. 

In the next place, wh&never a carriage-wheel, or horse's 
hoof, falls eccentrically*-.on a large stone, it is loosened 
from its place, and disturbs the smaller ones for a consid- 
erable distance around it, thus preventing their consol- 
idation. Therefore no large stones should he ever em- 
ployed. 

Small angular stones are the cardinal requisites. When 
of suitable materials of proper size, and applied in ac- 
cordance with the directions which will be presently given, 
they will unite and consolidate into one mass, almost as 
solid as the original ^tone, with a smooth, hard, and un- 
elastic surfa«^e. 



196 IMPROVEMENT OP THE SURFACE. 

We will examine successively the proper quality ol 
stone to be used ; the size to which they should be bro- 
ken ; the manner of breaking them ; the thickness of the 
coaling; the best method of applying the stone ; of rolling 
the road ; of keeping it in order ; and of repairing it when 
in bad condition. 

THE QUALITY OF THE STONE. 

The materials employed for a broken-stone road (often 
called the " Road metal") should be at the same time 
hard and tough. " Hardness is that disposition of a solid 
which renders it difficult to displace its parts among them- 
selves ; thus, steel is harder than iron, and diamond al- 
most infinitely harder than any other substance in nature. 
The toughness of a solid, or that quality by which it will 
endure heavy blows without breaking, is again distinct 
from hardness, though often confounded with it. It con- 
sists in a certain yielding of parts with a powerful general 
cohesion, and is compatible with various degrees of elas- 
ticity."* 

Some geological knowledge is required to make a 
proper selection of the materials. The most useful are 
those which are the most difficult to break up. Such are 
the basaltic and trap rocks, particularly those in which 
the hornblende predominates. The greenstones are very 
variable in quality.! Flint or quartz rocks, and all pure 
silicious materials, are improper for use, since, though 
hard, they are brittle, and deficient in toughness. Granite 
is generally bad, being composed of three heterogeneous 

* Sir John Herschel. " Discourse on the study of Natural Philosophy." 
.t The greenstone of Bergen and Newark mountain (near New York) 
ie good ; that of the eastern face of the Palisades above Weehawken is 
too liable to decomposition. (Renwick, Pract. Mechanics, p. 145.) 



MCADAM ROADS. 197 

materials, quartz, felspar, and mica, the first of which is 
brittle, the second liable to decomposition, and the third 
laminated. The sienitic granites, however, which con- 
tain hornblende in the place of felspar, are good, and bet- 
ter in proportion to their darkness of color. Gneiss is still 
inferior to granite, and mica-slate wholly inadmissible. 
The argillaceous slates make a smooth road, but one which 
decays very rapidly when wet. The sandstones are too 
soft. The limestones of the carboniferous and transition 
formations are very good ; but other limestones, though 
they will make a smooth road very quickly, having a pe- 
culiar readiness in " binding," are too weak for heavy 
loads, and wear out very rapidly. In wet weather they 
are also liable to be slippery. It is generally better econ- 
omy to bring good materials from a distance than to em- 
ploy inferior ones obtained close at hand. Excellent 
materials may be found throughout the primary districts 
of the United States. In the tide-water regions, south of 
New York, boulders, or rolled pebbles, must be employed. 

As the harder stones cost much more to break than the 
softer ones, the lower courses of the road may be formed 
of the latter, and the former reserved for covering the 
surface, which has to resist the grinding action of the 
wheels.* 

In alluvial countries, where stone is scanty and wood 
plenty, an artificial stone may be formed by making the 
clay into balls, and burning them till they are nearly vit- 
rified. The slag, or refuse, of iron furnaces, makes an 
excellent material. The stony or slaty part of coal may 



* This is the practice on the avenues of New York ; broken gneiss be- 
ing put below, and covered with broken boulders, which cost three times 
as much to break. 




198 IMPROVEMENT OF THE SURFACE. 

be used near collieries. Cubes of iron have been im- 
bedded among the stones with some advantages.* 

SIZE OF THE STONE. 

The stone should be broken into pieces, which are as 
nearly cubical as possible, (rejecting splinters and slices) 
and the largest of which, in its longest dimensions, can 
pass through a ring tioo and a half inches in diameter. 
In reducing them to this size, there will of course Fig. 108 
be many smaller stones in the mass. These are 
the proper dimensions, according to Telford and 
Parnell.\ Edgeworth prefers l^ inches. Pen- 
fold^ names two inches for brittle materials. If 
smaller they would crush too easily ; but on the 
other hand, the less the size of the fragments, the smaller 
are the interstices exposed to be filled with water and mud. 
The tougher the stone, the smaller may it be broken. 
The less its size, the sooner will it make a hard road ; 
and for roads little travelled, and over which only light 
weights pass, the stones may be reduced to the size of 
one inch. 

McAdam argues that the size of the stone used on a road 
must be in due proportion to the space occupied on a smooth 
level surface, by a wheel of ordinary dimensions ; and, as it 
has about an inch of contact longitudinally, therefore every 
stone in a road exceeding one inch in diameter, is mischievous ; 
for the one-sided bearing of the wheel on a larger stone will 
tend to turn it over and to loosen the neighboring materials. 
But this argument proves too much ; for however small the 
stone is, there must be a moment, just as the wheel is leaving 
it, when the pressure is one-sided, and therefore tends to over- 
turn it. Subsequently McAdam preferred the standard of 

» Parnell, p. 245. t Ibid. p. 133. t Pages 14, 15. 



McADAM ROADS. 



199 



weight to that of size, and made six ounces the maximum, 
(corresponding for average materials to cubes of 11 inches, or 
2\ inches in their longest diagonal) directing his overseers to 
carry a pair of scales and a 6-oz. weight, with which to try 
the largest stones in a pile. The weight standard has the ad- 
vantage, that the stones are smaller as they increase in speci- 
fic gravity, to which the hardness is generally proportional. 
He subsequently says that he had " not allowed any stone 
above three ounces in weight (equal to cubes of 1| inches, or 
2 inches in their longest diagonal) to be put on the Bath and 
Bristol roads for the last three years, and found the benefit in 
the smoothness and durability of the work as well as economy 
of repairs."* On examining old roads he found that the aver- 
age size of the stones varied from seven to twenty-seven ounces 
in weight, and that " the state of disrepair and the amount 
of expense on the several roads was in a pretty exact propor- 
tion to the size of the material used."f The French engineers 
value uniformity of size much less than McAdam, and call it 
" rather an evil than a good." They therefore use equall};- all 

sizes from 1\ inches to dust.J 

Fig. 109. 



BREAKING THE STONE. 

The weight and shape of the hammer, 
and the manner of using it, are of much 
importance, making a difference of at least 
10 per cent. The head of the hammer 
should be six inches long, and weigh about 
one pound ; and the handle be tough and 
flexible, and 3 feet long, if used standing, 
or 18 inches, if used silting, which is belter. 
The laborer sits before the pile, and breaks 
the stones on it, or on a large concave stone 
as an anvil, on which the stones to be bro- 

« Letter of 1834, in Am. Railroad Journal, Jan. 10, 1835. 
t System of Roadmakiug, 1825. | Gayffier, p. 201. 




200 IMPROVEMENT OF THE SURFACE 

ken are placed, resting only on their ends, so that, being 
struck sharply in their middle, they break into angular 
fragments. Children with smaller hammers can do the 
lighter work, so that a whole family may be employed. 
The workmen should not be paid by the day, but at an 
equitable price per cubic yard. A medium laborer can 
break in a day from 1 1 to 2 yards of gneiss ; but only J 
to I yard of hard boulders, or " cobble-stones." 

THICKNESS OF THE COATING. 

Twelve inches of well consolidated materials on a good 
bottom, will be sufficient for roads of the greatest travel, 
and will resist all usual weights, and frosts. In the cli- 
mate of France, ten inches is considered enough for the 
most frequented roads, and six or eight inches for others. 
The thickness should vary with the soil, the nature of the 
materials, and the character of the travel over it ; it should 
be such that the greatest load will not affect more than 
the surface of the shell ; and it is for this purpose chiefly 
that thickness is required, in order that the weight which 
comes on a small part only of the road may be spread 
over a large portion of the foundation. The severe frosts 
of our northern states require the maximum of depth.* 

McAdam advocates less thickness than the other Eng- 
lish constructors. He considers from 7 to 10 inches suffi- 
cient, calling the latter depth of " well consolidated mate- 
rials equal to carry any thing." He adds, " some new 
roads of six inches in depth were not at all affected by a 
very severe winter ; and another road having been allowed 

* Stone broken into fragments of from 1 to 6 inches occupies twice 
as much space as in the original solid state ; but the broken stone placed 
upon the road is reduced by the pressure of the wheels to two-thirds 
of its former bulk, or more exactly se-'en-tenths. 



McADAM ROADS. 201 

to wear down to only three inches, this was found suffi- 
cient to prevent the water from penetrating, and thus to 
escape any injury by frost." He earnestly advocates the 
principle that the whole science of artificial road-making 
consists in making a solid dry path on the natural soil, 
and then keeping it dry by a durable water-proof coating. 
" The broken stone is only to preserve the under road 
from moisture, and not at all to support the vehicles, the 
weight of which must be really borne by the native soil, 
which, while preserved dry, will carry any weight, and 
does in fact carry the stone road itself as well as the car- 
riages upon it." ..." The stone is employed to form a 
secure, smooth, water-tight flooring, over which vehicles 
may pass with safety and expedition at all seasons of the 
year." ..." Its thickness should be regulated only by 
the quantity of material necessary to form such a flooring, 
and not at all by any consideration as to its own indepen- 
dent power of bearing weight." ..." The erroneous 
idea that the evils of an undrained wet clayey soil can be 
remedied by a large quantity of materials, has caused a 
large part of the cosily and unsuccessful expenditures in 
making broken-stone roads,"* 

APPLICATION OF THE MATERIALS. 

The road-bed, having been thoroughly drained, must 
be properly shaped and sloped each way from the centre, 
so as to discharge what water may penetrate to it, and not, 
as is often practised, be made level, and the crowning 
given by a greater thickness of stone in the middle. 
Upon this bed, a coating of three inches of the clean bro- 
ken stones, free from any earthy mixture, is to be spread 

* McAdara — " System of Road-making," passim. 



202 IMPROVEMENT OF THE SURFACE. 

on a dry day. The travel is then to be admitted on it, 
men being stationed to rake in the ruts as soon as formed, 
or a heavy roller used, till it becomes almost consolidated, 
but not completely so, (the determination of this time being 
a nice and important practical point) and a second coat of 
three inches is then to be added during a wet time, as 
moisture greatly facilitates the union of the two. A third 
coat is added as was the second, and a fourth if that be 
required. If the stone be very hard, and the wheeling 
very difficult, fine clean gravel, free from earth, may be 
spread over the surface ; but it is better for the future 
solidity of the road to dispense with this, if possible. 

If a thick coat be laid on at once, there is a very great 
destruction of the material before it becomes consolidated, 
if it ever does so. The stones will not allow one another 
to be quiet, but are continually elbowing each other, and 
driving their neighbors to the right and to the left. This 
constant motion rapidly wears off the angular points, and 
reduces the stones to a spherical shape, which, in con- 
junction with the amount of mud and powder produced, 
destroys the possibility of any firm aggregation, and the 
road never attains its proper condition of hardness.* 

The broken stones need not be spread over a greater 
width than from 12 to 16 feet, (except near large cities) 
and " wings" of earth may be left on each side. For a 
road little used a single track of 8 feet of the " metal" will 
suffice.! 

The perfect cleanliness of the stones is strongly insisted on 
by McAdam. He directs the broken stones to be very carefully 
kept perfectly free from any mixture of earth, or any matter 
which will imbibe water, or be affected by frost ; since roads 

* Penfold, p. 15. t See page 47. 



McADAM ROADS. 203 

made with such a mixture become loose in wet w^eather, and al- 
low the wheels of carriages to displace the materials, and to cut 
through to the original soil, thus making the roads rough and 
rutty, the admission of water being the great evil. He adds 
that nothing must be laid on the clean stone under the pretence 
of " binding ;" for clean broken stone will combine by its own 
angles into a smooth solid surface, which cannot be affected 
by vicissitudes of weather, nor displaced by the action of 
wheels. 

The French engineers consider this cleanliness as unneces- 
sary, since the travelling on the road very soon pulverizes the 
materials, and fills the interstices with dust and mud ; though 
it might be replied that this took place only on the surface. 
Some of them, observing the large amount of vacant space in 
a mass of broken stone,* have even proposed to combine with 
it in advance a certain proportion of calcareous stone,f or even 
clay and sand.J just sufficient to fill up the existing vacancies. 
This would doubtless make a road tolerably fit for use much 
sooner than the regular plan, but its permeability to water 
would entail on it all the evils mentioned in the preceding par- 
agraph. 

* A cubic metre of broken stones, placed in a water-tight box, 
which they just fill, can receive in the empty spaces between the 
fragments a voUune of water = j^^g, or nearly one-half of the whole, 
the actual solidity of the stones being therefore only -^^-^. This does 
not vary for stones from 1 to 8 inches in aize. After prolonged travel 
it increases to y^g-, leaving a void of only -~^-^. For rolled pebbles 
and sand the actual solidity may be as much as y^%. For perfect 
spheres, calculation shows that the solidity of a mass of them in- 
creases as their diameter decreases. Thus, if a cubic metre be filled 
with spheres 4 inches in diameter, their solid volume will be y^,— ; if 
they are 1 inch in diameter their volume is --^ ; and if only J, inch, 
it is ■^-^^. Pebbles by theory, as well as by the experiment above 
cited, would be intermediate between broken stones and spheres. — 
(Gayffier, pp. 204 to 214.) 

+ M. Polonceau. M. Girard de Caudemberg. 



204 IMPROVEMENT OF THE SURFACE. 



The use of a very heavy roller will much facilitate the 
consolidation of the road. A plan highly recommended* 
is to have a roller made of a hollow cylinder, of cast iron, 
or covered with iron bands, seven feet in diameter, and 
five feet long. A strong axle passes through its length. 
Its ends are closed, and two interior partitions, perpendic- 
ular to the axis, divide it into three equal chambers. A 
longitudinal band of the surface, a foot wide, can be de- 
tached, so as to give access to the interior spaces, which 
are filled with gravel, one or all of them, according to the 
weight desired. The empty cylinder weighs 7000 lbs. ; 
each compartment filled with gravel adds 4,000 lbs. to 
the weight ; so that the entire weight may be made suc- 
cessively 7,000 lbs., 11,000 lbs., 15,000 lbs., and 19,000 
lbs. To compress a new road, ten or twelve strong horses 
should be attached, on a wet day in summer, to the eiwpty 
roller, and draw it several limes over every part of the 
road, till the materials have been so far compressed as not 
to form a ridge in front of the roller. Then the middle 
division is to be filled with gravel, (moistened, to give it 
solidity) and the rolhng resumed till the draught is so much 
lessened that the end divisions can be filled, the middle 
one being emptied at first if necessary. There should be 
an excess of power in the horses, so that they may do 
less injury by the violent pressures of their feet. Every 
part of the road should be passed over from 40 to 100 
times. To increase the stability of the compression ob- 
tained, an inch of gravel should be spread over the surface 
and passed over by the roller a few times. If the weather 

* Gayffier, p. 212. 



MCADAM ROADS. 205 

be dry, ilie surface should be watered. The season should 
be summer, that the road-bed may be dry, and the day be 
wet, to ensure a moist surface, which facilitates the bind- 
ing of the materials. 

When the rolling has finished the compression, the 
road is still very different from one which has borne the 
traffic of many years ; for although the materials are 
strongly pressed against one another, and have taken 
a stable position, they have not acquired the adhesion 
which takes place after a series of years. The new road, 
therefore, needs for some time most careful attention. 
The travel must finish it by being forced to pass over 
every part of it uniformly, heaps of pebbles being placed 
very irregularly, so as to direct the vehicles successively 
on all the points of the road. Every rut, and the slightest 
hollows and elevations, must be promptly removed by a 
liberal supply of laborers, whose work will, however, 
have been greatly lessened by the previous rolling. They 
must rake over every inequality of surface the moment 
that it is formed. 

KEEPING UP A ROAD. 

This is a very different thing from " repairing a road," 
though the two are often confounded. A due attention to 
the former will greatly lessen the necessity for the latter. 
The former keeps the road always in good condition ; the 
latter makes it so only occasionally, after intervals of va 
rious length, during which it is continually deteriorating 
in a geometrical ratio, so that the better the state in which 
the road is kept, the less are the injuries to it, and there- 
fore, tlie less the expense of keeping it in this excellent 
condition. 

" Keeping up the road" requires the daily attention of 



206 IMPROVEMENT OF THE SURFACE. 

a permanent corps of laborers. Supposing the road to be 
already in good condition ; that is, in proper shape, and 
free from holes, ruts, mud, and dust ; to keep it so, re- 
quires two fundamental operations : 

1, The continual removal of the daily wear of the ma 
terials, whether in the shape of mud or of dust ; 

2. The employment of materials to replace those 
removed. 

The first operation requires hoes and brooms. The 
hoes should be three feet long, and of wood, as iron ones 
would be more likely to loosen the stones. The lighter 
dust and more liquid mud must be swept off by birch 
brooms. The detritus between the little projections of 
the stones should not be removed by too thorough sweep- 
ing, as it protects them from immediate crushing, and 
preserves their stability. The broom is also necessary to 
remove every trace of wheels, the moment they have 
passed, so as to oppose that habit or instinct of horses 
which leads them to follow in the track of the preceding 
vehicle, and which would soon convert unremoved tracks 
into ruts. The broom and hoe have then a double end 
to be accomplished by the same operation, viz., effacing 
tracks and removing detritus. Very effective machines have 
also been constructed for accomplishing these purposes.* 

The second operation of applying new materials de- 
mands several precautions. To prevent a weak place 
from being neglected because the materials are not at 
hand, they should be kept in depots, never more than a 
quarter of a mile apart, and carried thence in barrows. 
They should be applied after a rain, as then they will 
more easily unite, and no coat, thicker than one stone, 



* Roads and Railroads, p. 91 



McADAM ROADS. 207 

should ever be applied at any one time. A cubic yard to 
a superficial rod will be quite enough at once. They will 
then soon become incorporated without having their angles 
worn out by motion, and will be of as much service as 
double the thickness applied at once. To avoid retarding 
the travel and increasing the draught too much, a new 
coat should not be put on any continuous space larger 
than six or seven square yards. If several depressions 
are found very near each other, cover the worst, and at- 
tend to the next after the first has become solid. The 
ruts which are formed should not be filled with loose 
stone, for this would make longitudinal ridges of harder 
material, but " the laborer should work the rake back- 
wards and forwards on each side of the rut and across it ; , 
and if he do it with his eyes shut, he will do more good, 
than by taking pains to gather all the stones he can find to 
place in it."* 

The number of men required by this system of con- 
stant watchfulness may at first seem an objection to it, 
but the expense will be amply repaid by the advantages 
obtained. Each laborer should have a certain length of 
the road assigned to his especial care, and the most intel- 
ligent and trustworthy among them should be made 
inspectors over the others for a certain distance. At 
times unfavorable for work on the road, they should be 
employed in breaking stone. The labor of one man will 
keep in repair three miles of well-made and well-drained 
road, for the first two years after its formation, and four 
miles for the next two years, by constantly spreading 
loose stones in the hollows, raking them from the middle 
to the sides, opening the ditches, &c. In the fifth year 



* Penfold, p. 20. 
14 



208 IMPROVEMENT OF THE SURFACE. 

some repairs, " with lifting," may be necessary, as ex- 
plained under the next head.* 

It will be seen by Morin's table, on page 63, that the 
friction or resistance to draught on a road with deep ruts 
and thick mud, is four times as great as on one in good 
order. This shows the importance of very perfectly 
" keeping up" the road. An incidental advantage is, that 
the prompt removal of the mud after every shower will 
prevent the annoyance of dust, so general an objection to 
McAdam roads, but not at all their necessary concom- 
itant. 

Where the materials of the road are very brittle stone, 
they wear away very rapidly in dr}?- weather, and their 
consumption may be much lessened by luatering the road 
judiciously ; not so little as to form a crust which adheres 
to the wheel, nor so much as to make the draught heavy. 
A moderate use of the watering cart preserves the mate- 
rials from pulverization, and keeps them settled in their 
places, at the same time that the comfort of the traveller 
is greatly enhanced. This is particularly necessary on 
roads in this country during our hot and dry summers ; 
for after a long drought the crust of the road sometimes 
becomes so dried out that it ceases to " bind," and per- 
mits loose stones to be detached from it, to the great 
injury of the surface. An excess of moisture must, how- 
ever, be avoided, since it increases the grinding power of 
the pulverized stones, as marble is sawn and jewels are 
cut with their own powder combined with water. 

The question may arise, whether the materials thus 
gradually added to the road, for alimentation rather than 
reparation, are sufficient to make up for its annual loss, 

» See Am. Railroad Journal, March 13, 1847. 



MCADAM ROADS. 209 

and diminution of depth, which is too small for direct 
measurement. Experiments upon this point indicate that 
the amount of materials annually consumed, and therefore 
to be replaced, is one cubic yard per mile* for each " col- 
lar," or beast of burden passing over it. Others consider 
it only two-thirds of a cubic yard.f 

REPAIRING A ROAD. 

A road properly kept up by daily attention, needs no 
repairs ; but if it be put in order only at intervals, the 
injuries to it, vi^hich have been increasing in geometrical 
progression, will render very serious repairs necessary. 
It will be found cut into ruts, deep holes, and irregular 
projections ; and often lower in the middle than at the 
sides. It must be put into shape, and restored to its 
proper cross-section, by cutting down the sides, and filling 
up the middle part. Only a single thin coat of stone 
should be applied at a time, — not more than a cubic yard 
to a rod superficial. The surface of the old road may be 
lightly picked up, or *' lifted," (with strong short picks) 
merely burying the point of the pick one or two inches 
deep, so that the new materials may be more readily 
united to the old ones. This is especially necessary on 
declivities, to prevent the stones rolling down the slope. 

When the road to be repaired is one which had been 
originally formed of large stones, and of superfluous 
thickness, no new materials should be brought upon it, 
but the old stones should be loosened with picks, gathered 
by strong rakes to the side of the road, and there broken 
to the proper size. The surface of the road having been 
put in proper shape, the broken stones are to be returned 

• Dupuis, Annales des Fonts et Chausees, 1842. t Gayffier, p. 232. 



210 IMPROVEMENT OF THE SURFACE. 

to it, being scattered uniformly and thinly over the sur 
face. Only a small space of road should be thus broken 
up at once, say six or eight feet in length, but the whole 
width. The old plan of repairing would be to fill up the 
holes with an additional supply of the same large mate 
rials ; but the method here recommended makes more 
work for men and less for horses, and produces a great 
saving in expense. 

The best season for repairing broken-stone roads is in 
the spring or early summer, when the weather is neither 
very wet nor very dry, for either of these extremes pre- 
vents the materials from, consolidating, and therefore pro 
duces either a heavy or a dusty road. If made at this 
season, the roads are left in a good state for the summer, 
and become consolidated and hard, so as to be in a condi 
tion to resist the work of the ensuing winter.* 

TELFORD ROADS. 

This name may be given to the roads of broken stone 
which rest on a peculiar pavement, as constructed by Tel- 
ford, on the Holyhead road and elsewhere, and of which 
he has given the following specification for a width of 
thirty feet. Fig. 110 is a section of the carriage-way of 
such a road. 

Fig. 110. 



" Upon the level bedt prepared for the road materials, 



* James Walker. 

t A bed with the same cross-section as the final road, would certainly 
be preferable, to ensure drainage. The pavement would then require to be 
of the same depth at centre and sides. 



TELFORD ROADS. 211 

a bottom course or layer of stones is to be set by hand in 
the form of a close, firm pavement. The stones set in 
the middle of the road are to be seven inches in depth ; 
at nine feet from the centre, five inches ; at twelve from 
the centre, four inches ; and at fifteen feet, three inches.* 
They are to be set on their broadest edges and lengthivise 
across the road, and the breadth of the upper edge is not 
to exceed four inches in any case. All the irregularities 
of the upper part of the said pavement are to be broken 
off by the hammer, and all the interstices to be filled with 
stone chips, firmly wedged or packed by hand with a light 
hammer, so that when the whole pavement is finished, 
there shall be a convexity of four inches in the breadth of 
fifteen feet from the centre. 

" The middle eighteen feet of pavement is to be coated 
with hard stones to the depth of six inches. Four of these 
six inches are to be first put on and worked in by car- 
riages and horses ; care being taken to rake in the ruts 
until the surface becomes firm and consolidated, after 
which the remaining two inches are to be put on. The 
whole of this stone is to be broken into pieces as nearly 
cubical as possible, so that the largest piece, in its longest, 
dimensions, may pass through a ring of two inches and a 
half inside diameter. 

" The paved spaces, on each side of the eighteen middle 
feet, are to be coated with broken stones, or well cleansed, 
strong gravel, up to the footpath or other boundary of the 
road, so as to make the whole convexity of the road six 
inches from the centre to the sides of it. The whole of 
the materials are to be covered with a binding of an inch 



* The curved section thus obtained, has been shown, on page 50, to be 
inferior to plane slopes on each side of the centre. 



212 IMPROVEMENT OF THE SURFACE. 

and a half in depth, of good gravel, free from clay or 
earth."* 

The propriety of this foundation, {^^ Bottoming,'''' or 
" Pitching'^) has been the subject of earnest controversy 
between the partisans of McAdam and those of Telford. 
The following are the defects imputed to a road of broken 
stones, laid on earth, (especially clay) without any foun- 
dation. 

The weight of vehicles forces the lower stones into the 
earth, which rises up into the interstices and forms a mix- 
ture of earth and stones which will always be loose and 
open, and never consolidate into a compact mass. In win- 
ter the water, which will penetrate, is frozen and breaks 
up the road. After a thaw and in wet weather, the road 
is a quagmire, the wheels cut deeply into it, and some 
times through the entire thickness, so that it resembles a 
ploughed field. At the best, after a rain the semi-fluid 
soil will rise up to the surface and form a coat of mud ; 
and after a drought the looseness of the stones will make 
them rub off their angles and soon wear out. Nor will 
any thickness of broken stones thoroughly destroy the elas- 
ticity of the soil, the evils of which were shown on page 58. 

McAdam maintains that thorough draining will prevent 
all these evils, but Telford thinks that they can be re- 
moved only by the " bottoming," for which he claims the 
following advantages. 

Roads, being in fact artificial structures, which have to 
sustain great weights and violent percussion, the first object 
must be to obtain a permanently firm and stable foundation. 

This is effected by the plan of " bottoming ;" for by it 
the pressure of the wheels is distributed over a large 

* Pamell, pp. 133-4. 



TELFORD ROADS. 213 

space. Suppose that the wheel touches and presses on a 
surface of 2 square inches. This pressure is carried to 
the foundation stones, which rest at their bottom on a broad 
surface, averaging 10 by 5 inches, or 50 square inches, 
so that each square inch of the soil receives only one- 
twenty-fifth part of the surface pressure, and there is 
therefore no danger of the pavement stones being pressed 
into it, nor of the soil being forced to ooze up between 
them. On a new embankment of soft earth it is best to 
lay brush or furze, and place the pavement upon this. 

The advantages of this system are most striking when 
the natural soil is retentive of moisture, as when it is clay. 
The pavement then acts as an under-drain to carry off the 
water which may find its way through the broken-stone 
surface. Even on a rock this pavement may be laid with 
advantage, to form a clear floor. 

When the stones are properly set, and wedged with the 
stone chippings, they will never rise to the surface.* To 
avoid disturbing them, the carts which bring the broken 
stone must not be allowed to pass over the foundation. 

From the moment that a road thus made begins to be 
used, it becomes daily harder and smoother. The strength 
of the resulting surface admits of carriages being drawn 
over it with tlie least possible distress to horses. The 
broken stones being on an immoveable dry bed, do not 

* Large stones, placed under a road and not thus wedged down, will 
invariably work up to the surface. Thus, over Breslington Common, 
England, the whole of the original soil had been covered at great ex- 
pense with large flag-stones, and the road-covering laid upon them. Their 
motion kept the surface in a loose, open state, till, on the road being dug 
open, they were found almost entirely turned vpon their edges, having 
been acting with the force of levers upon the road, which they had made 
to crack and sink, without the cause at such a depth being suspected. — 
McAdam. 



214 IMPROVEMENT OF THE SURFACE. 

mix with the soil, and become perfectly united together 
mto one solid mass. 

The parts of the Holyhead road formed with such a 
foundation, were unaffected by a series of unusually se 
vere frosts, followed by thaws and heavy rains, while the 
parts of it differently made, and other roads in the neigh- 
borhood, were broken up, and " became as bad as a 
bog."* 

A road thus constructed will in most cases cost less 
than one entirely of broken stone ; for the course of foun- 
dation-stones may be of any cheap and inferior stone, as 
sand-stone, &c., which will bear weight, and not be de- 
composed by the atmosphere, but which would not be 
sufficiently hard and tough for the broken-stone covering. 
The cost of hammering and setting this pavement will be 
less than that of breaking up an equal mass, and the total 
amount of stone employed will be no more than would 
have been required for a road entirely of broken stone. 

But even if such a road cost more at first, it would be 
cheaper in the end ; for, beside the saving of draught, 
stones laid on such a pavement last much longer than 
those laid on earth, two courses of the former outlasting 
three of the latter. The expense of scraping is lessened 
in the same or even a greater proportion. 

On the other hand, it is objected that, between the wheel 
above and the foundation-stone beneath, the broken stone 
will be in a situation like that of the grain between two 
millstones, and must therefore be more rapidly ground to 
powder than if on a soft bottom.f But this will be pre- 
vented by using harder stone for the surface than for the 
foundation. 

* Telford First Report on Holyhead roads. t Penfold, p. 8. 



TELFORD ROADS. 215 

McAdam also maintains that the materials last longer 
on a soft and elastic bottom than on a hard one ; and in- 
stances a road in Somersetshire, where a part of it is 
" over a morass so extremely soft that when you ride in 
a carriage along the road, you see the water tremble in 
the ditches on each side," and is succeeded by a bottom 
of limestone rock, continuing for five or six miles. An 
exact account of the expenditure on each having been kept, 
it was found that the cost of keeping up the soft was to 
that of the hard only as five to seven ; i. e. five tons of 
stone on the former would last as long as seven on the 
latter. But this seems an exceptional case, being con- 
trary to all other experience. Sir John Macneill testifies 
very strongly that the annual saving of a paved bottom 
will be one-third of the expense in any case, and that if 
the diminished amount of horse labor were considered, it 
would be very considerably more than that.* 

An artificial substitute for a pavement foundation, consist- 
ing of a concrete, or composition of Roman cement and gravel, 
has been employed with great success on a wet and elastic 
soil, where every thing else had failed, and where stones for 
bottoming would have been very expensive. The locality was 
the Highgate Archway Road near London, in a deep cutting 
between two high banks of clay, where the soil was surcharged 
with water. Many attempts at draining had been made, and 
a great thickness of broken stone had been used, and subse- 
quently relaid on furze and pieces of waste tin. But the stone 
mixed with the wet clay, and rapidly wore away, becoming 
round and smooth, without ever consolidating, and the road 
was almost impassable. The Parliamentary Commissioners 
finally took charge of it, and Sir John Macneill succeeded in 
making a perfect road. Four longitudinal drains were made 
the whole length of the road, cross drains at every 90 feet, and 
y 

* Parnell, p. 163. 



216 IMPROVEMEMT OF THE SURFACE. 

intermediate small drains at every 30 feet under the cement.* 
On the prepared centre, of eighteen feet in width, after it had 
been properly levelled, was put a layer, six inches thick, of 
the concrete, formed of one part of Roman cement, one of 
sand, and eight of stones. The sand and cement were mixed 
dry in a large shallow trough ; the gravel was added ; as little 
water as possible was used ; and the whole mixture was then 
cast upon the ground. Before it had set, a triangular piece of 
wood was indented into the surface, so as to leave, at every 
four inches, a triangular groove for the broken stones to lie 
in and fasten into. These grooves fell three inches from the 
centre to the sides of the road, in order to carry off any water 
which might percolate through the broken stones above it. Six 
inches of these were laid upon it when it had sufficiently hard- 
ened, (which was in about fifteen minutes) and the sides or 
wings were filled up with flint gravel. The concrete cost at 
that place 50 cents per square yard six inches thick. The 
object was to attain a dry and solid foundation for the broken 
stone. The result was an excellent road, undisturbed by se- 
vere frosts, and on which one horse could draw as much as 
three in its original state. 

4. PAVED ROADS.T 

A good pavement should offer little resistance to wheels, 
but give a firm foothold to horses ; it should be so durable 
as to seldom require taking up ; it should be as free as 
possible from noise and dust ; and vi^hen it is laid in the 
streets of a city, it should be susceptible of easy removal 
and replacement to give access to gas and w^ater pipes. 

A common but very inferior pavement, which disgraces 
the streets of nearly all our cities, is constructed of rounded 

* See Pamell, pp. 157 and 160, and plates to Simms on Roads. 

t Gayffier, pp. 193-8 ; Marlette, pp. 104-8 ; Jullien, pp. 316-18 ; Pamell, 
pp. 110-123, 348-359 ; Mahan, pp. 292-5 ; Journal of Franklin Insti- 
tute, Sept. Oct. 1843. 



STONE PAVEMENTS. 217 

water-worn pebbles, or " cobble-stones." The best are of 
an egg-like shape, from 5 to 10 inches deep, and of a 
diameter equal to half their depth. They are set with 
their greatest length upright, and their broadest end upper- 
most. Under them is a bed of sand or gravel a foot or 
two deep. They are rammed over three times, and a layer 
of fine gravel spread over them to fill their interstices.* 

The glaring faults of this pavement are that the stones, 
being supported only by the friction of the very narrow 
space at which they are in contact, are easily pressed 
down by heavy loads into the loose bottom, thus forming 
holes and depressions ; and at best offer great resistance 
to draught, cause great noise, cannot be easily cleaned, 
and need very frequent repairs and renewals.! 

The pavement ivhich combines most perfectly all desira- 
ble requisites, is formed of squared blocks of stone, rest- 
ing on a stable foundation, and laid diagonally. 

We will examine successively the merits of different 
foundations ; the quality of stone preferable ; their most 
advantageous size and shape ; their arrangement ; the 
manner of laying them ; their borders and curbs ; their 
advantages ; and their comparison with McAdam roads. 



* The following is part of the specification for the New York pavement : 
" The paving stones must be heavy and hard, and not less than six inches 
in depth, nor more than ten inches in any direction. Stones of similar 
size are to be placed together. They are to be bedded endv/ise in good 
clean gravel, twelve inches in depth. They shall all be set perpendicularly 
and closely paved on their ends, and not be set on their sides or edges iu 
any cases whatever." 

t The cost of such a pavement for a new street is in New York from 
50 to 75 cents per square yard ; for repairing an old street, about 20 cents. 



218 IMPROVEMENT OP THE SURFACE. 



FOUNDATIONS. 

The want of a proper foundation is one of the most 
frequent causes of the failures of pavements. A founda- 
tion should be composed of a sufficient thickness of some 
incompressible material, vsrhich vi^ill effectually cut off 
all connection betvi^een the subsoil and the bottom of the 
paving-stones, and should rest upon a well-drained bot- 
tom, for which in cities a perfect system of sewerage is 
indispensable. The principal foundations are those of 
sand, of broken stone, of pebbles, and of concrete. 

Foundations of sand. — This material, when it fills an 
excavation, possesses the valuable properties of incompres- 
sibility, and of assuming a new position of equilibrium 
and stability when any portion of it is disturbed. To se- 
cure these qualities in their highest degree, the sand 
should be very carefully freed from the least admixture of 
earth or clay, and the largest grains should not exceed 
one-sixth of an inch in diameter, nor the smallest be less 
than one-twenty-fifth of an inch. The bed of the road 
should be excavated to the desired width and depth, and 
be shaped with a slope each way from the centre, corres- 
ponding with that which is to be given to the pavement. 
This earth bottom should be well rammed, and a layer of 
sand, four inches thick, be put on, be thoroughly wetted, 
and be beaten with a rammer weighing forty pounds. 
Two other layers are to be in like manner added, and the 
compression will reduce the thickness of twelve inches to 
eight. The number of layers should be regulated by the 
character of the subsoil. Two inches of loose sand are 
to be then added to fill the joints of the stones, which may 
be now laid. The pressure of loads upon these stones is 
spread by the incompressible sand over a large surface 



STONE PAVEMENTS. 219 

of the earth beneath. This is the favorite system in 
France.* 

Foundations of broken stone. — A bed is to be excava- 
ted, deep enough to allow twelve inches of broken stone 
to be placed under the pavement. A layer of four inches 
is first put on, and the street then opened for carriages to 
pass through it. When it has become firm and consoli- 
dated, another layer of four inches is added and worked 
in as before ; and finally a third layer ; making in fact a 
complete McAdam road. Upon it the dressed paving- 
stones are set.t This method, though efiicient, is very 
inconvenient, from the length of time which it occupies, 
and the difficulty of draught while it is in progress. 

Foundations of pebbles. — Such a pebble pavement as 
is described on page 217, resting itself on sand, gravel, or 
broken stones, has been recommended to be adopted as 
the foundation of the dressed block pavement, for streets 
m which there is a great deal of travel.:j: 

Foundations of Concrete. — Concrete is a mortar of 
finely-pulverized quicklime, sand, and gravel, which are 
mixed dry, and to which water is added to bring the mass 
to the proper consistence. It must be used immediately. 
Beton (to which the name of Concrete is often improperly 
given) is a mixture of hydraulic mortar with gravel or 
broken stone ; the mortar being first prepared, fine gravel 
mcorporated with it, the layer of broken stones subse- 
quently added to a layer of it 5 or 6 inches thick, and the 
whole mass rapidly brought by the hoe and shovel to a 
homogeneous state. Three parts of sand, one of 
hydraulic lime, and three of broken stone is a good pro- 
portion. A mixture of one part of Roman cement, one of 

* Gayffier, p. 126. t Pamell, p. 117. 

% Committee of Frauklin Institute, and Parnell, p 116. 



220 IMPROVEMENT OF THE SURFACE. 

sand, and eight of stone, has also been employed very 
successfully. Beton is much superior to Concrete for 
moist localities.* 

The excavation should be made fourteen inches lower 
than the bottom of the proposed pavement, and filled with 
that depth of the concrete or beton, which sets very rap- 
idly, and becomes a hard, solid mass, on which a pave- 
ment may then be laid. This is, perhaps, the most 
efficient of all the foundations, but also the most costly at 
first, though this would be balanced by its permanence 
and saving of repairs. It admits of access to subterrane- 
ous pipes with less injury to the neighboring pavement 
than any other, for the concrete may be broken through 
at any point without unsettling the foundation for a con- 
siderable distance around it, as is the case with founda- 
tions of sand or broken stones ; and when the concrete is 
replaced, the pavement can be at once reset at its proper 
level, without the uncertain allowance for settling which 
is necessary in other cases. The blocks set on the con- 
crete are usually laid in mortar. We will examine pres- 
ently the propriety of this. 

QUALITY OF STONE. 

The stone should be of a kind which will not wear 
smooth, but which will always remain rough on the sur- 
face. Many varieties of granite are of this character, and 
are therefore very suitable. The hardest stones are the 
best, and their specific gravity is a tolerable test of their 
hardness. The hardest stones will also absorb but ^Iq 
of their volume of water ; tender ones will absorb ^V* 
The hardest stones also, when struck by a hammer, give 
a clearer and more ringing sound than soft ones. Tender 



STONE PAVEMENTS. 221 

Stones may be made mucli more durable by plunging 
them in boiling bitumen, which penetrates their pores and 
prevents them from absorbing water, which is the most 
powerful agent in their disintegration. 

SIZE AND SHAPE. 

The size of the stones should be proportioned to the 
number and weight of the vehicles which will pass over 
them, and as each stone is liable to have resting upon it 
the entire weight borne by one wheel, it should be large 
enough to sustain this weight without being crushed, or 
depressed. It should also be no larger than a horse's 
hoof, so as to prevent any shpping upon its surface, even 
where unbroken by joints ; but the fulfilment of the first 
condition will generally make this impossible, and the se- 
lection of a proper quality of stone will render it unneces- 
sary. If stones of different dimensions are admitted, they 
should be assorted, and only those of the same size should 
be used near each other, or the small ones will sink be- 
low the rest, and the depressions thus formed will be in- 
creased by every passing wheel. It is therefore very 
desirable that they should be uniform in size. Cubes of 
eight inches in every direction seem to combine most of 
these requisites. They should be very slightly tapering 
towards their lower ends, thus making them truncated 
pyramids.* If they are much larger than this standard, 
the weight of a wheel coming on one end of one of them, 
will tend to depress it and to elevate the other end, so 



* Blocks of this size cost in Philadelphia delivered on the street, $2.75 
per square yard of surface. Laying a bed of gravel 15 inches deep, set- 
ting the stone, &c., cost 50 cents more, making the entire cost of the 
pavement $3.25 per square yard. 



222 



IMPROVEMENT OF THE SURFACE. 



that such large stones would be less firm than smaller 
ones. 

Hexagonal blocks have been suggested, and would 
form a more compact mass than those of any other shape ; 
but their superiority in this respect would probably not 
compensate for the extra cost of cutting them. 



ARRANGEMENT. 



Fig. 111. 



1 1 1 1 M 1 M 1 


1 M M 1 M 1 1 1 


Vn 1 1 M M 1^ 


iVlVn Mill 




1 ' t V 1 1 1 1 1 111 


Vl'i'l 1 1 MM 



The rectangular stones may 
be laid in continuous courses 
across the road, but so as to '^ 
"break joints" in the direction ^\, 
of its length, as shown in Fig. 
111. It has been observed, how- 
ever, that when stones are laid, as is usual, with their 
joints parallel and perpendicular to the direction of the 
road, they wear away most rapidly upon the edges which 
run across the road, since these receive most directly the 
shocks of the wheels, and that the stones thus become 
convex. To prevent this, and ^'g- H^. 

to secure equal wear, they 
should be laid so that the joints 
cross the road obliquely, ma- 
king an angle of 45° with the 
axis of the roadway. One set 
of joints may be continuous, 
but the others should break 
joints, as in Fig. 112. 

Oblong stones are preferred by the French engineers, 
with their upper surfaces nine inches by five and a half. 
They should be laid, (if not diagonally) so that their great- 
est length is across the street, their narrowest dimension 
being that passed over by the wheels. They thus offer less 




STONE PAVEMENTS. 



223 



resistance to draught than cubical 
blocks, according to the experi- 
ments of Morin. 

In the steep streets of Genoa 
the stones are laid in oblique 
courses, pointing up the ascent, 
and meetingat an angle in the cen- 
tre. The continuous joints, which 
descend to the right and to the 
left, facihtate the discharge of the 
rainwater. 



Fig. 113. 




MANNER OF LAYING. 

The top surface of the foundation (of whatever mate 
rial it may be) which forms the bed for the paving-stones, 
is to be shaped, as directed on page 50, sloping each way 
from the centre, with inclinations ranging from 1 in 50 to 
1 in 100, flatter in proportion to the smoothness of the 
surface. The stones should be so set that the joints be- 
tween them will not exceed one quarter of an inch. But 
as they are not cut regularly enough to touch on every 
part of their surface, some substance must be interposed 
to All up the vacancies, and to enable them to support 
each other. Mortar is used for this purpose on founda- 
tions of concrete, and even on those of sand and broken 
stone. Sometimes gravel is put between them, and a 
grouting of lime-water poured in. Iron chippings are 
added to the gravel to increase the adherence. But no 
adherent compound, such as these, can resist the con- 
tinual vibrations and play of the pavement. Some other 
substance should therefore be employed, which will 
change its position of equilibrium, and never cease to fill 

up the spaces between the stones, whatever shocks they 

15 



224 IMPROVEMENT OF THE SURFACE 

may receive. Such a substance is pure sand. The 
quality necessary has been indicated on page 218. A 
coating of an inch should also be spread over the stones. 
When the foundation is any thing but concrete, the paving- 
stones must be rammed, after a certain portion has been 
laid, with a maul weighing 60 lbs., and those which break 
under this must be replaced, and those which sink, taken 
up and reset. 

BORDERS AND CURBS. 

When the paved road forms the middle portion, or 
causeway, of a wider road, with wings of earth or broken 
stone on each side of it, its edges must be supported 
against the lateral thrust of the stones, by borders of larger 
blocks, 9 or 10 inches wide, 13 to 18 inches long, and 13 
inches deep. They are laid as headers and stretchers, so 
as to form a bond with the pavement. Their outer edge 
should also have occasional projections into the wings, so 
that a rut may not be there formed. 

When the pavement is a city street, the curb-stones 
should be long blocks.* 
There should be no gut- , , . 



ter or other channel than '^^^^^^rf"^3^^„^^^ 



that formed, as in the "^^^^^^^^^^^^ 

ngure, by the meetmg oi ^yTmrnm^w 

the inclined pavement with the curb-stone, which should 
rise 6 or 8 inches above the pavement, and be sunk as deep 
into the ground as possible. The foot pavements should 



* In the specifications for the New York pavements, the Curb-stones 
are required to be not less than 3 feet long, 5 inches thick, and 20 inches 
wide ; and the Gutter-stones to be not less than three feet long, 6 inches 
thick, and 14 inches wide. 



STONE PAVEME>fTS. 225 

incline towards the street at the rate of one inch in ten 
feet, or 1 in 120.* 

ADVANTAGES. 

The advantages of such a pavement are its smoothness 
and uniformity of surface, enabhng vehicles to be drawn 
over it with ease to the horses, comfort to the passengers, 
and but little wear and tear of the carriages, which can 
be therefore made much lighter than at present. At the 
same time it gives a good foothold to the horses ; causes 
very little noise, yet enough to warn the foot-passengers 
of the approach of a vehicle, and is very easily cleaned 
of the dirt which may collect upon it. It is also very 
durable, thereby rendering umiecessary the frequent stop- 
page of a street for repairs ; and though at first more 
expensive than cobble-stones, is finally far more eco- 
nomical. 

PAVED AND MoADAM ROADS COMPARED. 

McAdam maintains that his roads are preferable to 
pavements, even for the streets of cities. He argues that 
they are cheaper, as requiring no more stone than pave- 
ments, admitting an inferior quahty, and costing less for 
repairs ; and that they give greater facility of travelling, and 
cause less annoyance from dust, when properly swept and 
watered. But experience in the streets of London shows 
the cost of broken -stone roads to be far greater than 
pavements, to which they are inferior in every respect.f 
The result of very full discussions at the Civil Engineers' 
Institution was, that a whin or granite pavement, of proper 
form and depth, laid on a sound bottom, is preferable to 



22(5 IMPROVEMKNT OF THE SURFACE. 

any other plan for carriageways in the metropolis and 
other large cities. The objections to the broken-stone 
roads are that they cannot resist the pressure caused by a 
very great intercourse, being liable to be thereby crushed 
and ground into dust, which is easily converted into mud ; 
that this hasty and continual destruction and renewal 
would, in a great city, prove intolerably troublesome and 
expensive, while the dust in dry weather, and the mud in 
wet, would greatly incommode the intercourse in the 
streets, as well as private dwellings and public shops. 
The surface of broken stone is also more injurious to the 
feet of horses than a good pavement, and less easy for 
their labor ; and the expense of making and maintaining 
the former would be at least fifty per cent, more than the 
latter.* 

ROMAN ROADS. 

The ancient Roman roads, which, even at the present 
aay, after the lapse of nearly two thousand years, may be 
traced for miles, as perfect as when first constructed, 
were essentially dressed-stone pavements, with founda- 
tions of concrete, resting on sub-pavements. The most 
perfect modern constructions thus appear to be only im- 
perfect and incomplete imitations. The direction and 
length of the intended road were marked out by two 
parallel furrows, from the space between which the loose 
earth was removed. The foundation of the road {Statu- 
men) was composed of one or two courses of large flat 
stones, laid in mortar, a bed of which was first spread 
over the earth. Next came a course of concrete (Rudus) 
formed of broken stones mixed with quicklime, and 

* Telford in Parnell, p. 351. 



/ ROMAN ROADS. 227 

pounded with a rammer. If the stones were freshly 
broken ones, three parts of them were mixed with one of 
quickUme ; if they were from old buildings, two parts of 
lime were used to three of the rubbish. The third course 
(Nucleus) was composed of broken bricks, tiles, and pot- 
tery, mixed with lime, which formed one-fourth of the 
whole. The mixture was spread in a thin layer, and in it 
were imbedded, so that their top surfaces were perfectly 
level, the large blocks of stone {Su?nma crusta) which 
formed the pavement. These stones were irregular poly- 
gons, usually with 5, 6, or 7 sides, rough on their under 
side, but smooth on top, and so perfectly fitted together 
that . the joints were scarcely perceptible. The entire 
thickness of the four strata was about three feet. When 
the road passed over marshy ground, the foundation 
stones rested on a framework of timber, (made of a 
species of oak not subject to warp or shrink) and to pro- 
tect this from the lime, it was covered with a bed of 
rushes or reeds, and sometimes of straw. On each side 
of the road were paved footpaths, and parapets ; with 
stones at regular intervals for mounting on horseback 
Milestones marked the distances to all parts of the empire 
from the Milliarium aureum, a gilt column in the Forum 
of Rome. 

The Russ Pavement, so deservedly popular in New York, is construct- 
ed thus :— The street (Broadway) is graded with a crown of 7 inches = 
Jg. Granite chips are spread over this, and rammed down flush with the 
earth. / A concrete foundation, 6 inches thick, is formed in rectangular 
sections. ' It contains 1 part of Rosendale cement, 2i parts of clean 
coarse sand, 2^ of broken stone, and 2 of gravel. On it rest rectangular 
blocks of sienitic granite, 10 inches deep, 10 to 18 long, and 5 to 12 wide. 
They are laid diagonally, at angles of 45° with the line of the street, and 
BO as to form lozenge-shaped compartments. Lewis holes in certain 
blocks, and iron plates under them, give easy access to water and gas 
pipes, permitting excavations 4 feet long, and 3^ wide. The contract 
price in 1849 was $5.50 per square yard of pavement 



228 



IMPROVEMENT OF THE SURFACE. 



6. ROADS OF WOOD. 

The abundance, and consequent cheapness, of wood 
m our new country, renders its employment in Road- 
making of great value. It has been used in the form of 
logs, of charcoal, of planks, and of blocks. 



LOG ROADS. 



Fig. 115. 



m?- 




When a road passes over soft 
swampy ground, always kept moist 
by springs, which cannot be drain- 
ed without too much expense, and 
which is surrounded by a forest, it 
may be cheaply and rapidly made 
passable, by felling a sufficient 
number of young trees, as straight 
and as uniform in size as possible, 
and laying them side by side across 
the road at right angles to its length. 
This arrangement is well known 
under the name of a " Corduroy''' road, of which the 
figure gives a top and end view. Though its successive 
hills and hollows offer great resistance to draught, and 
are very unpleasant to persons riding over it, it is never- 
theless a very valuable substitute for a swamp, which in 
its natural state would at times be utterly impassable. 
But necessary and desirable as these roads may be to 
accomplish such an end in the infancy of a settlement, 
their retention upon a great thoroughfare is a disgraceful 
proof of indolence and want of enterprise in those who 
habitually travel over them ; though several such instances 
might be specified. 



CHARCOAL ROADS. 229 

CHARCOAL ROADS. 

A very good road has been lately made through a 
swampy forest, by felling and burning the timber, and 
covering the surface with the charcoal thus prepared. 

" Timber from six to eighteen inches through is cut 
twenty-four feet long, and piled up lengthwise in the 
centre of the road about five feet high, being nine feet 
wide at the bottom and two at the top, and then covered 
with straw and earth in the manner of coal-pits. The 
earth required to cover the pile, taken from either side, 
leaves two good-sized ditches, and the timber, although 
not split, is easily charred ; and, when charred, the earth 
is removed to the side of the ditches, the coal raked 
down, to a width of fifteen feet, leaving it two feet thick 
at the centre and one at the sides, and the road is 
completed." 

A road thus made in Michigan cost $660 per mile, 
and is said to be very compact and free from mud or 
dust. At a season when the mud on the adjoining earth 
road was half axletree deep, " on the coal road, there was 
not the least standing, and the impress of the feet of a 
horse passing rapidly over it was like that made on hard 
washed sand, as the surf recedes, on the shore of the lake. 
The water was hot drained from the ditches, and yet there 
were no ruts or inequalities in the surface of the coal 
road, except what was produced by more compact pack- 
ing on the line of travel. It is probable that coal will 
fully compensate for the deficiency of limestone and gravel 
in many sections of the west, and, where a road is to be 
constructed through forest land, that coal may be used at 
a fourth of the expense of limestone." 

Two such roads in Wisconsin were let by contract at 
$1.56 and $1.62i per rod, or $499 and $520 per mile. 



PliANK ROADS. 

Plan and Cross Section of a Planh Road. 
Fiff. 115. a. 



Fig. 115, b 



Ul 



Fig. 115, a, Cross-section. 
Fig. 115, b, Plan, or Top View. 

Scale, 10 feet to 1 inch. 



^ 



The most valuable improvement since McAdam's, and 
one superior to his in many localities, is the recent in- 
vention of covering roads with planks. The first plank 
road on this continent was constructed in Upper Canada 
in 1836. A short piece, laid down experimentally, gave 
so much satisfaction, as to ease of travelling, and cheap- 
ness of keeping in repair, that a mile of it was construct- 
ed the next year at a cost of $2100. Its success caused 
it to be continued. Since then 500 miles have been 
constructed in Canada, and more than 2000 registered 
in the State of New-York ; and probably several thou- 
sands more in the other states of the Union from Maine 
to Texas and Wisconsin. 



PLANK ROADS. 231 

In the most generally approved system, two parallel 
rows of small sticks of timber (called indifferently sleep- 
ers, stringers, or sills) are imbedded in the road, three or 
four feet apart. Planks, eight feet long and three or four 
inches thick, are laid upon these sticks, across them, at 
right angles to their direction. A side track of earth, to 
turn out upon, is carefully graded. Deep ditches are dug 
on each side, to ensure perfect drainage ; and thus is 
formed a Plank Road. 

The benefits of covering the earth with some better 
material have been indicated on page 188, and the pecu- 
liar advantages of this plank covering will be more fully 
made known, when we shall have discussed in order the 
various details of construction.* 

LAYING THEM OUT. 

The waste of labor caused by unnecessary ascents m 
a road, has been pointed out in the early part of this vol- 
ume, (pages 32-36.) It was also shown (page 28) that 
it is profitable to the traveller to go two or three thousand 
feet around to avoid ascending a hill a hundred feet high ; 
though the cost of constructing the additional length of 
road partially counterbalances this consideration. It was 
also proved that the smoother the surface of the road was 
made, the more injurious proportionally were such as- 
cents. They are therefore especially objectionable on 
plank roads, which hold an intermediate place between 
common roads and railroads. Some distinguished engi- 

* Hon. Philo White's report to the Council of Wisconsin, February, 
1848, embodies a very extended and systematic collection of information 
on this subject. To it, and to the valuable published and obliging private 
communications of Hon. George Geddes, C. E., (who first introduced and 
naturalized this improvement in the United States,) the author is much 
indebted, as also to many other recent sources. 



232 IMPROVEMENT OF THE SURFACE. 

neers have been led astray on this point. Their argu 
ments, if carried out to their full extent, would lead to the 
construction of railroads also with similarly steep grades. 
It is true, as they state, that a given load can be drawn 
up a much steeper hill on a plank road than on a corn 
mon one, the friction on the former being so much less, 
but (as proven on pages 34 and 35, which see) this will 
lessen in an equally increased ratio the advantages of the 
level portions of the road. Let us assume the resist- 
ance of friction, or " stick-tion," (as Professor Whewell 
calls it,) on a plank road to be one-third of that on a good 
earth road. It will therefore be one-sixtieth of the weight 
carried, if that of the earth be one-twentieth. If, now, a 
horse can draw one ton on the level earth road, the total re- 
sistance will be doubled when he comes to a hill which rises 
one foot in going twenty, (1 in 20,) and he will be able 
to draw only half a ton up this hill, and therefore his load 
on the level parts of the road would be but half a ton ; 
for it would be useless for him to take more to the hill 
than he could drag up it. Now suppose the same road 
to be planked, and this hill to remain untouched. On 
the level portions the same horse can now draw three tons, 
Dy our hypothesis. But the hill, rising 1 in 20, will offer a 
resistance three times as great as does the " stiction" of 
the plank road, and the whole resistance in going up it will 
therefore hefow times as great as on a level. The horse 
can therefore draw only one-fourth of his former load, or 
only three-quarters of a ton, which is consequently the limit 
of his load on the level. Thus then this hill has brought 
down the gain of the plank road over the earth to only a 
quarter of a ton, instead of two tons, which it would be, 
were the hill removed. Therefore, in laying out a plank 
road, it is indispensable, in order to secure all the benefits 



PLANK ROADS. 233 

which can be derived from it, to avoid or cut down all 
steep ascents. 

A very short rise, of even considerable steepness, may, 
however, be allowed to remain, to save expense ; since a 
horse can, for a short time, put forth extra exertion to over- 
come such an increased resistance ; and the danger of 
slipping is avoided by descending upon the earthen track.* 

A plank road, lately laid out, under the supervision of 
Mr. Geddes, between Cazenovia and Chittenango, N. Y., 
is an excellent exemplification of the true principles of 
roadmaking. Both these villages are situated on the 
" Chittenango creek," the former being 800 feet higher 
than the latter. The most level common road between 
these villages rises, however, more than 1,200 feet in go- 
ing from Chittenango to Cazenovia, and rises more than 
400 feet in going from Cazenovia to Chittenango, in spite 
of this latter place being 800 feet lower. It thus adds 
one-half to the ascent and labor, going in one direction, 
and in the other direction it goes up hill one-half the 
height, which should have been a continuous descent. 
The line of the plank road, however, by following the 
creek, (crossing it five times,) ascends only the necessary 
800 feet in one direction, and has no ascents in the other, 
with two or three trifling exceptions, of a few feet in all, 
admitted in order to save expense. There is a nearly 
perpendicular fall in the creek of 140 feet. To overcome 
this, it was necessary to commence, far below the falls, to 
climb up the steep hill-side, following up the sides of the 
lateral ravines, until they were narrow enough to bridge, 
and then turning and following back the opposite sides till 
the main valley was again reached. The extreme rise is 
at the rate of one foot to the rod, (1 in 16^ ;) and this only 

* The steeper the grade, the more rapid is the wear of the planks, in a very remark- 
able degree ; a foot In a rod doubling the wear on a level. 



234 IMPROVEMENT OF THE SURFACE. 

for short distances, and in only three instances, with a 
much less grade, or a level, intervening. The hne passes 
through a dense forest, which supplied its material, being 
cut into plank by sawmills erected in a gulf never before 
approached by a wheeled carriage. 



A single track of plank, eight feet wide, with an earth- 
en turn-out track beside it, of twelve feet, will in almost 
all cases be sufficient. This gives twenty feet for the 
least width necessary between the inside top lines of the 
ditches, the width of which is to be added, making about 
two rods on level ground. If extra cuttings or fiUings be 
required, the width occupied by their slopes must be add- 
ed to this. An earthen road of eight feet wide on each 
side of the plank track, has sometimes been adopted. The 
New York general plank road law fixed four rods {66 
feet) as the least permissible width that plank roads might 
be laid out. This provision has since been repealed. 

Wider plank tracks were at first employed. In Can- 
ada single tracks were made from 9 to 12 feet wide. But 
it was found, on the 12-feet Toronto road, after seven 
years' use, that the planks were worn only in the middle 
seven or eight feet, and that the remaining four or five 
feet of the surface had not even lost the marks of the saw. 
One-third of the planking was therefore useless, and one- 
third of the expenditure wasted, 

A double plank track will rarely be necessary. No 
one without experience in the matter can credit the amount 
of travel which one such track can accommodate. Over 
a single track near Syracuse, 161,000 teams passed in 
two years, averaging over 220 teams per day, and durmg 
three days 720 passed daily. The earthen turn-out track 



PLANK ROADS. 235 

must, however, be kept in good order, and this is easy, if 
It slope off properly to the ditch, for it is not cut with 
any continuous lengthwise ruts, but is only passed over 
by the wheels of the wagons which turn off from the 
track, and return to it. They thus move in curves, which 
would very rarely exactly hit each other, and this travel, 
being spread nearly uniformly over the earth, tends to 
keep it in shape rather than to disturb it. 

If, however, there is so much travel that the earth track 
will not remain in good order, then this travel will pay for 
the double track which it requires. But this should be 
made in tiuo separate eight-feet tracks, and not in one 
wide one of 16 or 24 feet, as was at first the practice. 
On a wide track the travel will generally be near its 
middle, and will thus wear out the planks very une- 
qually, besides depressing them in their centre, and ma- 
king the ends spring up, and when it passes near one end 
that will tilt up, and loosen the other. Besides, when a 
light vehicle wishes to pass a loaded one moving in the 
centre, as it naturally will, the former will be greatly de- 
layed in waiting for the other to turn aside, or else will 
have one wheel crowded off into the ditch. But where 
there are two separate tracks, the whole width of one is 
at the service of the light vehicle. On a sixteen-feet track 
near Toronto, the planks, having become loose and un- 
settled, were sawn in two in the centre, and this imper- 
fect double track, even without any turn-out path be- 
tween, worked better than in its original state. An 
experienced constructor states that if he were desired to 
build a road fifty feet wide, he would make it in separate 
eight-feet tracks. 

The wide track of 16 feet plank has sometimes been 
divided into two of eight feet, by spiking down scantling 



236 IMPROVEMENT OF THE SURFACE. 

20 feet long, and six inches square, along the middle of 
the road, at intervals of 100 feet in the clear, between 
each scantling. This, however, only partially remedies 
the objections adduced. 

When the ground is of such a very unsettled and yield- 
ing nature, such as loose sand, marsh, &c., that a solid 
turn-out track of earth cannot be made, planks, sixteen 
feet long, may be used, resting on three, four, or five 
sleepers, crowning in the middle three or four inches, and 
the ends sprung down, and pinned to the outer sleepers. 

GRADING. 

The importance of elevating a road-bed above the level 
of the adjoining fields, and digging deep ditches on each 
side, has been already urged, (pages 53, 54,) and this is 
a fundamental requisite in making a good plank road. 
Employ the earth from the ditches, if good material, re- 
jecting the sods, to raise the road-bed. Give the ditches 
free outlets, cut their bottoms with true slopes, make under- 
drains, of cobble-stones and brush, across the road in wet 
places, and use every precaution to ensure thorough and 
complete drainage. This will be more difficult in a flat 
than in a hilly country. If it be effected, however, the 
plank will last much longer, and the road be always in 
better condition.* 

The " cross-section" of the road-bed, or its shape cross- 

* The ditches and side slopes of the road-bed, after being ploughed up, 
may be most rapidly shaped by the use of a scraper of this form, 5>, 
composed of two planks hinged together in front, and kept apart in the 
rear by an adjustable cross-piece. The team is attached to the outer 
plank at such a distance from the point as to keep the inner plank in the 
direction of the road, so that it forms the straight edge of the bank, while 
the skew of the outer plank throws the earth to one side in the manner 
of a snow-plough. A man with a long lever inserted in the outer side 
regulates this more exactly. 



PLANK ROADS. 237 

wise, between the ditches, must be carefully adjusted so 
as to freely carry off the rain which may fall on it. First 
decide on which side of the road the plank track is to be 
laid. It should generally be on the right-hand side com- 
ing from the country into a town, so that the farmers' 
wagons may keep upon it, when they bring in their heavy 
produce, and that the turning out may be done by those 
which are going back light.* The twelve feet width in- 
tended for the earth track should be heavily rolled or beat- 
en, to make it firm and hard. It should slope down from 
the centre three-quarters of an inch to the foot, (1 in 16,) 
and the eight feet of plank should fall off three inches, or 
1 in 32. From each side of the 20 feet thus graded, the 
bank should slope down to the bottom of the ditches at 
the rate of three inches to the foot, or 1 in 4. (See Fig. 
115, a; page 230.) 

The proper shape may be most easily and accurately 
given by the use of a common masons level, having a 
tapering piece of wood under it, (as shown in Fig. 88, 
page 173,) or having one leg so much longer than the 
other, as will give the slope required. If the plank be 
laid on an old roadway, no more of it should be broken 
up than is absolutely necessary for imbedding the sleep- 
ers, as it is very desirable to preserve as solid a founda- 
tion as possible. 

SLEEPERS, SILLS, OR STRINGERS. 

Material. — Pine, hemlock, tamarack, oak, and walnut, 
nave been used in Canada. Hemlock has been mostly 
used in New York, from its abundance and cheapness. 
Pine would be more durable. 

Number and size. — At first, five or six, each six inches 
square, were placed under 16 feet plank. The Canada 

* But, in ascending a long hill in either direction, it should be on the right- 
hand side. 



238 IMPROVEMENT OF THE SURFACE. 

Board of Works' Specification, 1845, directs four to be' 
put under a 16-feet road, and three under a 10-feet road; 
the outer ones to be five inches square, and the inner ones 
to be six inches wide, and two inches thick, laid flatwise. 
On the New York roads of eight feet planks, two sleep- 
ers, four inches square, have been generally employed. 
They have, however, been found insufficient, and the ex- 
perienced engineer of the original Syracuse road, strongly 
recommends sleepers 12 by 3, laid on their flat sides, and 
for an important road would make them 1 2 by 4, or even 
12 by 6.* They should be large and strong enough to 
hold up the plank road in case of a soft place for a few 
feet. Others argue, however, that they should be small 
enough to sink down with the earth as it settles under the 
planks, so thatthesemay continue to bear upon the ground; 
as otherwise the planks would be rapidly worn out by the 
springing thus caused, and would be soon rotted by the 
confined air under them. They also assert that the only 
use of the sleepers is to keep the road in shape when first 
laid down. Indeed, a road three miles long has been laid 
in Canada, without any sleepers at all under the planks, 
and it worked quite well. Its advocates say tliat sleepers 
form a trench in which water collects, and is by theni pre,'- 
vented from running off. .-It therefore floats the planks, or 
washes out mud from under them, and thus forms a cav- 
ity, which produces the bad effects above mentioned. This 
consideration would make light sleepers appear to be worse 
than none. The conclusion seems to be that large sleep- 
ers should be used for an important road ; and that for a 
poor one, which expects to receive only light loads, and 
which runs over a hard bottom, sleepers might perhaps 
be altogether dispensed with. 

* The lower sleeper may be 14 inches wide, and the other 10, as the former acts 
as a bridge over the channels made under it to let off the water ; and also sustains a 
somewhat larger share of the weight. 



PLANK ROADS. 239 

Length. — The sleepers used should be as straight and 
true as possible. On the Syracuse road none less than 
13 feet long were admitted. On the Canada roads they 
are required to be not less than 16 feet, nor more than 20 
feet long. 

Laying. — Their distance apart, centre to centre, should 
be such that the wheels of loaded wagons may pass di- 
rectly over their middle ; or somewhat nearer to their 
outer than their inner sides. This distance will therefore 
vary in different sections of the country, according to the 
usual " track" of wagons.* If this principle be varied 
from, it should be by bringing the sleepers nearer the 
middle than the ends of the planks, to prevent any de 
pression in the centre. The foot-wide sleepers in the 
figure are drawn three feet apart in the clear, or four feet 
centre to centre. 

They should be well bedded in the earth, in trenches 
cut to receive them, with their top surface barely in sight. 
They should bear firmly and evenly throughout their 
whole length, and the earth between them be well ram- 
med down, and made firm, solid, and even.f The sleeper 
nearer the ditch is to be laid so much lower than the 
inner one, as to give the proper slope to the road, 
which is so important for carrying off the rainwater. 

Joints. — At the joints, where two sleepers come to 
gether, end to end, they are liable to sink under passing 
loads. To prevent this, various means may be employed. 

* The common track of wagons, measured "from inside to outside," 
which is the same as from centre to centre, is four feet eight inches in the 
state of New York. In New Jersey and the Southern States, it is five feet. 
In Connecticut it varies from three feet eight inches for light wagons, to five 
feet two inches for heavy ones. In Wisconsin, it is five feet four inches. 

t A wooden roller, weighing two tons, has been very successfully used 
for settling the sleepers and the earth between them, being drawn over 
them several times before they are planked. 



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240 IMPROVEMENT OF THE SURFACE. 

The broad sleepers (12 by 3) may be sawn in two length- 
wise, so as to be each 6 by 3, and laid side by side, so as 
to " break joints ;" the joints of one set being opposite 
the middle of the adjoining pieces, which form the other 
set. This arrangement is shown in Fig. 115, b, page 230. 
The sawmills charge no more for the sleepers in two 
pieces, each 6 by 3, than in one 12 by 3. A second 
remedy is to lay a ng.ns^c, 
short board under the 
joints of the sleepers, 
as shown in Fig. 115, 
c. A third is to con- 
nect the ends by a " " ®' 
mortice and tenon, two 
inches long, as in Fig. 115, d. A fourth is to unite them 
by a bevel scarfing, three inches in length, reversed on 
each half, as shown in Fig. 115, e, in which, for distinct- 
ness, the two sleepers are represented as separated. In 
every case the joint on one side of the road ought to be 
opposite the middle of the sleeper on the other side. 



Material.— In Canada, pine, hemlock, tamarack, oak, 
and walnut, have been employed. In this State, hemlock 
alone has been used, being the cheapest material to be 
obtained. Its defects are its perishable nature, and its 
numerous, knots, which soon make the road rough, when 
the softer portions of the planks have worn away. Pine, 
oak, maple, or beach, would be preferable. In Wiscon- 
sin, &c., white and burr oak are abundant, and would 
therefore be advantageously used. Oak would make the 
most permanent road, from its superior capabilities of re- 
sisting both wear and decay. From its greater weight it 



PLANK ROADS. 241 

would cost a little more for hauling and handling. The 
slipperiness of hardwood has been made an objection to 
it, but the sand with which the road should be covered, 
would obviate this. Whatever sort of limber is em- 
ployed, it should be sound, and free from sap, bad knots, 
shakes, wanes, or any other imperfections. The plank 
should be full on the edges, and not less than nine nor 
more than sixteen inches wide, if of soft wood, or not more 
than twelve, if of hard wood. 

Thicliness. — The planks are usually either three or four 
inches thick ; but the builders of the later roads prefer 
giving less strength to the plank, and more to the sleep- 
ers, which are more durable ; and therefore recommend 
three-inch plank, with sleepers a foot wide. With hem- 
lock plank, any thickness beyond three' inches is wasted, 
for when two inches have been worn :down, the projecting 
knots will make the road too rough to travel on, and it 
will require renewal. One inch more will be sufficient to 
hold the knots in, so that we get three inches as the prop- 
er thickness.* With less knotty timber, thicker plank may 
be used, provided there will be travel enough to wear out 
the whole thickness from above, before it unprofitably rots 
out from below. When two tracks are laid, that which 
would be travelled by the loaded wagons going to market 
may be laid with four-inch plank, and the other track, for 
the light wagons, with three-inch plank. 

Laying. — The planks should be laid directly across the 
road, at right angles, or " square," to its line, as shown in 
Fig. 115, b, on page 230. The ends of the planks are 
not laid evenly to a line, but project three or four inches 
on each side alternately, so as to prevent a rut being 
formed by the side of the plank track, and to make it 
easier for loaded wagons to get upon it ; as the wheels, 

* Tho knots may, however, be cheaply dabbed down with an adze. 



S^42 IMPROVEMENT OF THE SURFACE. 

instead of scraping along the ends of the planks, when 
conaing towards the track obliquely after turning off, will, 
on coming square against the edge of one of these pro- 
jecting planks, rise directly upon it. On the Canada roads, 
every three planks project three inches on each side of 
the road alternately, as shown in Fig. 115, b. 

The planks were laid lengthwise of the road, on the 
first one running from Quebec, it being supposed that they 
would wear better, and could be more easily taken up and 
replaced. But it was found that loaded horses slipped 
upon them, (the longitudinal direction of the grain giving 
no hold to the feet,) that ruts were soon worn in them, 
and that they did not keep their places. This arrange- 
ment is therefore now abandoned. 

The planks have also been laid obliquely, diagonally, or 
" skewing ;" so as to make an angle of 45 degrees with 
the line of the road, twelve feet plank making an eight- 
feet wide road. This plan is adopted on the Longeuil 
and Chambly road near Montreal. Its advantages are, 
that the edges of the plank are not worn down so soon as 
when the wheels strike them directly, (as was shown in 
reference to pavements, on page 222 ;) that the zigzag 
ends of the plank facilitate the getting on the track ; and 
that there is less loss on the rejected, or " cull" planks of 
12 feet, than on those of 8 feet. But when a wagon- 
wheel comes upon one end of a plank laid thus obliquely, 
the other end, having no load to keep it down, will spring 
up, if not fastened to the sleeper ; and if it is, the spikes 
or pins will finally be loosened. Each end of each plank 
undergoes this action in turn, and thus the road is injiired 
and broken up. The first method of laying the planks — 
at right angles to the direction of the road — is much to 
be preferred. 



PLANK ROADS. 243 

The planks must be laid so as to bear equally on the 
sleepers, and on the ground between thena, depending 
chiefly on the latter for their support. The earth mus* 
be well up to and touching the planks at every point, lor 
if any space of confined air be left, dry rot soon follows 
If any water be allowed to get under the planks, it forms 
a soft mud, which is pressed up between them, and de- 
posited on their surface, thus excavating a cavity under 
them, and rendering them liable to move under passing 
loads in a manner which soon wears them out. They 
must also be laid to close joints.* 

Fastening. — On the Canada roads the planks have 
generally been spiked or pinned down to the sleepers. 
The specification of the Board of Public Works directs 
them to be spiked " with one spike at each end for planks 
12 inches wide or less, and two at each end for planks of 
a greater width. The spikes are to be of the description 
called ' pressed' spikes, made of the best English or Ca- 
nadian iron. They are to be 6^ inches long, f inch 
square, with chisel-shaped edges, and good broad heads, 
and are to weigh five to a pound. They are to be driven 
with the chisel-edge across the fibres of the wood." 

On the New York roads this has been considered an 
unnecessary expense, since the loads come equally upon 
both ends of the transverse planks, and thus tend to keep 
them down in their places, their own weight assisting in 
this. But in wet, and badly-drained places, a new con- 
sideration intervenes. If the planks are not fastened down, 
they will float as soon as an inch of water gets under 
them. The wheels of a loaded wagon pressing down 
each plank in turn, drive the water before them, till it 
finally attains force enough to throw up a plank, and thus 
break up the road. On the other hand, when the planks 

* Never allow the earth on the sides of the track to rise above the ends of the plank. 



244 IMPROVEMENT OF THE SURFACE. 

are fastened down, the whole road is floated, and the vi- 
brations produced by the passing loads drive the water out 
on the sides and top of the road, and excavate cavities, 
which ought to be immediately filled up, an operation 
which is made difficult by the fastening down of the planks 
to the sleepers. It is therefore thought better to leave 
the plank free, and allow them to be thrown out of place, 
and thus at once give free passage to the water, and pre- 
vent further mischief ; a repairer being kept constantly at 
work upon the road, and required in rainy weather to .pass 
over every portion of it once or twice a day. It might be 
well, as a compromise, to spike down planks at short in- 
tervals, say every fifth or tenth plank, the rest being well 
driven home against these. 

Covering. — The planks having been properly laid, as 
has been directed, should be covered over one inch in 
thickness, with very fine gravel, or coarse sand, from 
which all stones, or pebbles, are to be raked, so as to 
leave nothing upon the surface of the road, that could be 
forced into and injure the fibres of the planks. ; The grit 
of the sand soon penetrates into the grain of the wood, 
and combines with the fibres, and the droppings upon the 
road, to form a hard and tough covering, like felt, which 
greatly protects the wood from the wheels and horses' 
shoes. Sawdust and tan-bark have also been used. 

The road is now ready for use. 



The chief items in the cost of a plank road are the tim 
ber and the earth-work. The price of the former wil' 
vary greatly in different localities and at different times. 
The cost of the latter, as well as of bridges, culverts, &c., 
will generally be different on every mile of road. The 



PLANK ROADS. 245 

cost of plank roads in general, therefore, cannot be defi- 
nitely stated. The following estimate gives the extremes. 
On the plan recommended, the planking will require, 
per mile, 8 x 3 x 5280 = 126,720 feet ; and the sleepers 
(2) XI x3 X 5280 = 31,680 feet; in all 158,400 feet; 
or, say, 160,000 feet, board measure. Shaping the road- 
bed, and laying the sleepers and planking, costs from 30 
cents to $1 per rod, according as the line is new, or on an 
old bed, and the soil easy or hard to work. The number 
oi gate-houses will be governed by the opposing consider 
ations of making them many, so that no one can travel far 
on the road without paying therefor ; and few, so that the 
expenses of collection may be small. By the New York 
Plank Road law, the toll-gates are not to be within three 
miles of each other. The item of contingencies will not 
bear any relation to the varying cost of the plank, and 
therefore should not be estimated by a percentage, as is 
usually done. These points being premised, we arrive 
at the following estimate of Cost 'per mile : 

Plank: 160 M. ; $4 to $10 per M.; . $640 to $1600 

Shaping and Laying ; 30 cents to $1 per rod, 96 " 320 

Gate-houses : per mile, .... 50 " 150 

Engineering and superintendence, . . 100 " 100 

Contingencies, . . . . . . 100 " 200 

$986 to $2370 

We thus see that the cost per mile will range from, say, 
$1000 to $2400, exclusive of extra earth-work, bridges, 
culverts, &c. From 10 to 15 cents per cubic yard may 
be estimated as the cost of the excavation, including put- 
ting it into emhanhnent, except when carried over one or 
two hundred feet, (see page 132;) and it should be stip- 
ulated that no cutting of less than two feet depth, should 



246 IMPROVEMENT OF THE SURFACE. 

be counted, or paid for, as " excavation ;" but be cori- 
sidered as included in the general price for laying. In 
making a new road through a forest, the clearing and 
grubbing will be a new item of expense. Add ten per 
cent, upon the cost of these items for contingencies inci- 
dent to them. The land is supposed to be given. 

The Syracuse and Central Square plank road, 16 
miles, cost 81487 per mile, with lumber at $5.20 per M. 
It has a single eight-feet track, except over a few spots of 
yielding sand. The Rome and Osivego road, 62 miles, 
cost $80,000, or about $1300 per mile ; lumber costing 
from $4 to $5 per M. It is of eight feet hemlock plank, 
three to four inches thick ; with grades cut down to 1 in 
20 near Rome, and at the western end, where it is more 
hilly, to 1 in 165-. The Utica northern road, 22 miles, 
cost $42,000, (besides $8000 for right of way over a turn- 
pike,) being nearly $2000 per mile, five miles being a new 
line cut through woods, at an extra cost for clearing, of 
$500 per mile. Deduct this, and the average cost would 
be about $1800 per mile. A short road near Detroit, 
eight feet wide, laid on a travelled roadway, cost, with 
lumber at $6 per M., $1500 per mile. 

The first New York road (Syracuse and Central 
Square) was not built by contract, but by days' work, so 
as to ensure the perfect bedding of the timbers. It was 
also found that the work was done at a less cost than the 
bids of contractors, who made such offers as would se- 
cure them against loss in a work then new and untried. 
In a road where there was much earthwork, that at least 
should be let by contract. The road should also be divided 
into quarter-mile sections, and the lumber for each be 
contracted for, to be equally distributed along the line, 
when delivered. The actual laying upon the graded bed 



PLANK ROADS. 247 

could then be done by days' work. All the operations 
should be under the charge of an intelligent and efficient 
engineer. 

DURABILITY. 

A plank road may require renewal, either because it 
has been worn out at top by the travel upon it, or because 
it has been destroyed at bottom by rot. But, if the road 
have travel enough to make it profitable to its builders, it 
will wear out first ; and if it does so, it will have earned 
abundantly enough to replace it twice over, as we shall 
see presently. The liability to decay is therefore a sec- 
ondary consideration on roads of importance. 

Wear. — The actual wear is of course proportioned to 
the amount of travel. The most definite results have 
been obtained on the first New York road, that from Syr- 
acuse to Central Square. In its first two years, ending 
July, 1848, more than 160,000 teams passed over its first 
eight miles. This travel wore its hemlock plank down 
one inch, where they had not been floated. Another inch 
could be worn down before the projections of the knots 
would make it necessary to relay the road, so that it 
would have borne the passage of 320,000 teams. But 
this is an under-estimate, inasmuch as the wear and tear 
of the first year is more than that of several following ; 
since the first travel upon the road tears off the outer 
splinters and fibres cross-cut by the saw, while the 
coating subsequently formed protects the plank from 
wear. Upon a Canada pine road, travelled over by at 
least 150 two-horse teams per day, (50,000 per year,) the 
road had worn down in two years only one-quarter of an 
inch ; and this too was attributed chiefly to its exposure 
the first year without sanding. It was estimated that 



248 IMPROVEMENT OP THE SURFACE. 

sanded plank on this road would wear at least ten years. 
Oak would of course wear longer. 

Decay. — As to natural decay, no hemlock road has as 
yet been in use long enough to determine how long the 
plank can be preserved from rot. Seven years is per- 
haps a fair average. Different species of hemlock vary 
greatly ; and upland timber is always more durable than 
that from low and wet localities. The pine roads in 
Canada generally last about eight years, varying from 
seven to twelve. The original Toronto road was used 
chiefly by teams hauling steamboat wood, and at the end 
of five years, began to break through in places, and, not 
being repaired, was principally gone at the end of ten 
years. Having been poorly built, badly drained, not 
sanded, and no care bestowed upon it, it indicates the 
minimum of durability. Oak plank cross-walks in De- 
troit, the plank being laid flat on the ground, have lasted 
two or three times as long as those of pine. It is be- 
lieved that oak plank, well laid, would last at least 12 
or 15 years. One set of sleepers will outlast two plank- 
ings ; several Canada roads have been relaid upon the 
old sleepers, thus much lessening the cost of renewal. 

A Canadian engineer thinks that $20 per mile would 
be required the first year ; to restore the grade where 
it had settled, to fasten loose plank, &c. For the next 
five years, $10 per mile, and then there would be some 
planks to be replaced. The repairs would then increase, 
so as to amount to a renewal of the surface at the 
end of four years more, making ten for the age of the 
road. 



PLANK ROADS. 249 



ADVANTAGES. 



Plank roads are the Farmer's Railroads. He profits 
most by their construction, though all classes of the 
community are benefited by any such improvement, 
as has been fully shown in the " Introduction" to this 
volume. The peculiar merit of plank roads is, that the 
great diminution of friction upon them makes them more 
akin to railroads than to common roads, with the advan- 
tage over railroads, that every one can drive his own 
wagon upon them. Their advantages naturally divide 
themselves into two classes; their utility to the commu- 
nity at large, and their profits to the stockholders who 
build them. 

1. To the community. A horse can draw on a plank 
road from two to three times as much as he can on an 
ordinary Macadam or good common road. On the latter 
roads one ton is a fair load for a single horse, and 3000 
lbs. the utmost allowance. But upon a plank road, a 
two-horse team has drawn six tons of iron ; another has 
drawn, for several days in succession, over two cords of 
green beech and maple wood, estimated at six tons also, 
and could draw four or five tons, thirty miles a day con- 
tinuously. These results of experience agree with the 
calculations founded on the data of p. 62, taking the fric- 
tion on a Macadam road at 3^-, (the average of the tw^o 
values there given,) and that on planks at gV- The re- 
sulting ratio is 2f to 1. 

A great degree of speed can also be obtained upon 
plank roads with much less. injury to the vehicles and to 
the horses feet than on a Macadam road, though contrary 
impressions have sometimes been caused by the excessive 
speed with which their light draught often causes horses 
to be driven, without the driver being aware of it. Eight 



250 IMPROVEMENT OF THE SURFACE. 

feet of a Canadian McAdamized road, disrupted by- 
frost, was taken up, and planked over ; and the horses 
when reined from the plank to the stone, in turning out, 
would of their own accord, if not prevented, immediately 
turn back upon the plank. 

But the peculiar advantage to the community of plank 
roads is their continuing in perfect order, and affording 
undiminished facilities for travel, at all seasons, while 
common roads are rendered impassable by the continued 
rains of autumn, the occasional thaws in mid-winter, or 
the " breaking up" in spring. They thus enable the 
farmer to carry his produce to market at seasons and 
in weather when he would otherwise be imprisoned at 
home, and could not there work to advantage. His farm 
will therefore be made more valuable to him ; and it 
has accordingly been found that the value and price 
of lands contiguous to those roads have been enhanced 
by their operation to such a degree as to excite the envy 
and complaints of those living off their line. The les- 
sened " stiction" will also enable him to carry his former 
load to a more distant market, if desired, or to carry to 
his former market a larger load, and therefore at less 
cost per bushel, hundred-weight, or cord. He can there- 
fore sell cheaper, and yet gain more. The consumer 
of his produce, wood, &c., gets a better supply of all 
articles, and at lower prices. The shopkeepers carry on 
an active trade with their country customers, at times 
when, were it not for these roads, they would have noth- 
ing to do. It is one of those few business arrange- 
ments by which all parties gain, and which, therefore, 
in the words of Clinton, actually " augment the pubUc 
wealth." 



PLANK ROADS. 251 

2. To the stockholders. The annual profits of a 
plank road will of course be governed by the two ele- 
ments of its first cost, and the amount of travel upon it. 
The latter should be approximately determined in ad- 
vance, as directed on page 66, One important point 
has, however, been determined with considerable accu- 
racy, viz. : how much a road will earn before it is worn 
out. Upon the first eight miles of the Syracuse and 
Central Square plank road, the tolls during its first two 
years, ending July, 1848, amounted to $12,900, and the 
expenses for salaries and repairs to $1,500; leaving 
$11,400 for dividends and rebuilding. This amount of 
travel had worn the plank down one inch. Another inch 
could be worn down before a renewal would be neces- 
sary, and the road would then have earned $22,800 
above expenses, or $2,850 per mile. This experience 
indicates that hemlock plank before being worn out, will 
earn two or three times their original cost. The surplus 
above the cost of renewal will therefore be payable in 
dividends, amounting in gross to between 100 and 200 
per cent, upon the first cost of the plank, (that of the 
whole road bearing no constant ratio io this ;) the amount 
of each annual dividend being of course greater the more 
rapidly this wearing out, with its concomitant and pro- 
portional earning, takes place. 

This calculation is predicated on the tolls established 
by the New York Plank Road law, which are as follows : 
For any vehicle drawn by two horses, &c., 1| cents per 
mile, and ^ cent for each additional animal ; for vehicles 
drawn by one horse f cent per mile; for a horse and 
rider, or led horse, ^ cent ; for every score of sheep, 
swine, or neat cattle, one cent per mile. But the com- 



252 IMPROVEMENT OF THE SURFACE. 

panies are not to charge more than will enable them to 
pay annual dividends of 10 per cent, upon the stock actu- 
ally paid in and expended on the road, after keeping the 
road in repair, and setting aside 10 per cent, for its re- 
construction. This restriction has since been repealed.* 

The great objection to plank roads in the eyes of an 
engineer is their perishable nature, and consequent final 
destruction. But this fault is one not peculiar lo plank 
roads, but common to all in a greater or less degree. 
Thus in the case of broken-stone, or McAdam roads, 
usually cited as contrasting models of durability, we find 
that they wear away so rapidly as to require not only con- 
stant repairs, but, when well kept up, an actual addition 
to their substance of one cubic yard per mile for each 
beast of burden passing over them, (see page 209;) and 
the 80,000 teams per year which passed over the Syra- 
cuse road, would have required an amount of broken 
stone, to replace their wear, enough to renew it many 
times over. A Canadian report to the Board of Public 
Works shows that the cost of one mile of McAdam road 
will there make and maintain nearly four miles of plank 
road ; and on one road the substitution of plank for bro- 
ken stone effected a saving of an amount sufficient to re- 
plank the road every three years, if that had been ne- 
cessary. The New York Senate report states that a 
plank road over the same line with a McAdam one can 
often be built and maintained for less than the interest on 
the cost of a McAdam one, added to the expense of its 



* The New York Laws relating to Plank Roads, are — 1847, chapters 
210, 287, 398 : 1848, chapt. 360 : 1849, chapt. 250. 



WOODEN PAVEMENTS. 253 

necessary annual repairs. But even if a plank road w^as 
still more perishable than it is, and was worn out in one 
year, still, if in that time it had repaid its cost two or 
three fold, (as we have seen it would do,) it would be so 
much the more profitable investment ; and this is the 
final object of all private engineering constructions. 

It should not be forgotten by the engineer engaged in 
laying out a road for a private company, that their inter- 
ests, and those of the public who are to use the road, are 
not identical. The public wish the road to be so laid out 
that they can carry over it the greatest possible loads at 
the least possible cost. The stockholders generally wish 
only to secure to themselves the largest possible amount 
of tolls in return for the smallest possible investment. 
These two interests conflict. The steep ascents, so in- 
jurious to the travelling public, as shown on pp. 231-3, 
are advantageous to the company who plank the road, 
since they prevent large loads being carried, and thus 
produce a twofold gain — the amount of tolls being pro- 
portioned to the number of the loads, and not (as they 
should be) to their weight ; and the carriage of such ex- 
cessive ones as would break defective plank being thus 
prevented. The engineer of the company must therefore 
sacrifice the absolute perfection of his road to this requisi- 
tion of policy, and may leave steep ascents untouched, thus 
saving the first cost of cutting them down, as well as in- 
creasing the subsequent receipts. But, on the other hand, 
if the grades of the road be not sufficiently improved, it 
may not attract the expected amount of travel. A pru- 
dent compromise must therefore be made between these 
opposing interests 



254 



IMPROVEMENT OF THE SURFACE. 




WOODEN PAVEMENTS. 

Pavements formed of wooden blocks, 
usually hexagonal in shape, possess 
many advantages. They cause little 
resistance to draught ; are almost en- 
tirely free from noise ; are easily 
kept clean ; are easy to a horse's hoof; 
lessen very much the wear and tear 
of vehicles ; are pleasant to travel- 
lers ; admit of great speed, and are cheaper in their first 
cost than granite blocks. 

To counterbalance these recommendations, they are 
slippery and therefore dangerous in wet weather ; and are 
very perishable, both from wear and from decay. The 
slipperiness has been obviated by grooving and striating 
their surface, but this lessens their ease of draught and 
noiselessness, and increases their cost.* The rapidity of 
their wear may be lessened by setting them on a founda- 
tion of broken stone, or of concrete, so shaped as to rap- 
idly drain the water from their bottoms ; and by covering 
their surfaces with a mixture of boiling tar and clean 
gravel. Their decay may be prevented by various chem- 
ical preservatives, of which the principal are, Kyan's, who 
saturates the wood with a solution of bichloride of mer- 
cury or corrosive sublimate (one pound to five gallons of 
water) ; Burnett's, who uses a solution of chloride of zinc, 
(one pound to ten gallons of water) absorbed in a vacuum ; 
Renwick's, with coal tar ; and Boucherie's, with the im- 
pure pyrolignite of iron, absorbed by the vital action of 
the sap vessels. 



* A description of various forms proposed for wooden pavements may 
be found in the N. Y. American Repository, vol. iii. ; and in London Me- 
chanics' Magazine, and Repertory of Patent Inventions, passim. 



KOADS OF BRICKS, CONCRETE, ETC, 



255 



6. HOADS OF OTHER MATJ3RIALS, 




Roads are made in Holland of hard burnt bricks, or 
" clinkers," laid on a firm foundation, and set on edge, 
with their longest dimension across the road. A better 
bond would be obtained by F'g- H'''- 

such an arrangement as is 
shown in the figure. But 
the pressure of heavy loads 
and the blows of horses' 
feet are too powerful for 
bricks, which should therefore be reserved for foot-pave- 
ments only. 

CONCRETE. 

Roads of concrete, or beton, six to eight inches thick, 
(such as has been described as the best foundation for 
granite blocks) have been warmly advocated in France, 
particularly for the use of steam carriages, in the place 
of the more costly, though more perfect railroads. Con- 
crete will sustain great weights, carried on wheels, with 
little injury, but has been found (on the towpath of a ca- 
nal aqueduct) to be rapidly destroyed by the feet of 
horses. 

CAST IRON. 

This material has been tried several times, but aban- 
doned in consequence of its wearing so smooth as to 
cause horses to slip. 

11 



256 IMPROVEMENT OF THE SURFACE. 



ASPHALTUM, 

This name has been given to a bituminous mastic, of 
which the principal locahties are Seyssel in France, and 
Val-de-travers in Switzerland. A limestone is also there 
found, which contains from 3 to 15 per cent, of bitumen. 
The stone is broken into fragments of the size of an egg, 
and ground to powder. A certain proportion, usually 
from 6 to 10 per cent., of mineral tar (obtained by boiling 
in water the bituminous sandstone of the same place) is 
combined with the limestone, by heating the former in 
iron boilers, and gradually adding and stirring in the 
powdered stone. In this state it is poured upon a level 
surface, and forms smooth cakes, over which gravel is 
spread. It is too weak for carriage-ways, and in this 
climate too soft in summer, and too brittle in winter, for 
even foot-pavements ; but in Paris the asphaltum side- 
walks of the Boulevards are most perfect specimens of 
pavements. The asphaltum is melted on the spot in 
large caldrons, and poured within a moveable frame to the 
desired thickness. The edges of these slabs are united 
with the same material, and the pavement before an en- 
tire block of houses is thus made one smooth level sur- 
face, unbroken by a single joint. 

CAOUTCHOUC. 

A pavement, formed by mixing gravel with melted 
caoutchouc, or gum elastic, has been tried in London. A 
specimen in the court-yard of the Admiralty, in 1844, 
was very pleasant to walk upon, but showed permanent 
depressions where heavily loaded vehicles had passed 
over it. 



KOADS WITH TRACKWAYS. 257 

7. ROADS WITH TRACKWAYS. 

When wheeled carriages are drawn by horses, the 
wheels should move on the smoothest and hardest sur 
face possible, while the horses require one rough enough 
to give them a secure foothold, and soft enough to be 
easy to their feet. These two opposite requirements are 
united only in Roads ivith Trackways, on which two 
parallel tracks of suitable materials are provided to re- 
ceive the wheels, while the space between the tracks is 
filled with a different material, on which the horses travel. 
The wheel-tracks are usually of stone, of wood, or of iron. 

STONE TRACKWAYS. 

The Egyptians seem to have first discovered the value 
of stone trackways in moving great weights, for traces of 
such contrivances have been found in the quarries which 
supplied the enormous stones of their Pyramids. In 
modern times they reappeared in the streets of Pisa, and 
are now general in those of Milan. They have of late 
years been used with great advantage in London, upon a 
road over which 250,000 tons annually passed, in wagons 
carrying each five tons. The repairs of this road for 
thirteen years cost less than one hundred dollars. The 
friction upon this stone trackway was so much reduced 
(being only yl-^ of the weight) that a small horse (weigh- 
ing 4^ cwt.) could draw on a level 15 tons ; and a pow- 
erful horse (weighing 14 cwt.) 30| tons, at the rate of 4 
miles per hour. On this road the tracks were blocks of 
granite, 5 or 6 feet long, 16 inches wide, and 12 inches 
deep. The space between them was paved.* 

» PameU, p. 106 



258 



IMPROVEMENT OF THE SURFACE. 



A similar trackway of stone has been used with great 
advantage to facih'tate the ascent of a steep hill, as a sub 
stitute for reducing the inclination. Upon the Holyhead 
road, two hills, each a mile in length, had an inclination 
of 1 in 20. To reduce this to 1 in 24 would have cost 
$100,000. Nearly the same advantage, in diminishing 
the tractive force required, was obtained by moderate 
cutting and embankment, and making stone trackways, at 
a total expense of less than half the former amount. To 
draw one ton over the original hills required a power of 
294 lbs. ; to draw it over the trackways laid on the same 
inclinations required only 132 lbs.; so that the tractive 
force was reduced more than one-half by this improve- 
ment ; and the effect was tlie same as if the hill had been 
cut down to a level, its surface remaining unchanged. 
The arrangement of this trackway is shown in Fig. 118. 

Fig, 118. 







The blocks were of granite, twelve inches deep, fourteen 
inches wide, and not less than four feet long. A foundation 
for them was prepared by making an excavation, 8 feet wide 
and 25 inches deep. On its levelled bottom was laid a rough 
pavement (like that described for the " Telford road," page 
210) eight inches deep. The joints were also filled with 
gravel. Upon this pavement were laid three inches of broken 
stones, none exceeding one and a half inches in their longest 



ROADS WITH TRACKWAYS. 259 

dimensions. On them was a layer of two inches of the best 
gravel, over which a heavy roller was passed. Upon this the 
stone blocks or " trams" were laid to a very accurate level. 
The spaces between and outside of them were filled up to a 
depth of six inches with broken limestone. On each side of 
the blocks was placed a row of paving-stones of granite, six 
inches deep, five inches wide, and nine inches long. The re- 
maining space was filled up with hard broken stone, and the 
whole covered with a top dressing of an inch of good gravel.* 

WOODEN TRACKWAYS. 

In districts where timber abounds, it may be substituted 
for stone in forming tracks, on which the wheels of or- 
dinary vehicles may run. Projections on the sides of the 
tracks may be employed to retain the wheels upon them, 
but the moisture retained in the joints would cause rapid 
decay, and if any such precaution be thought necessary, 
a furrow or gutter in one of the tracks would be prefera- 
ble.! It would of course be necessary in this case, that 
the road should everywhere have sufficient inclination to 
carry off the water, which would otherwise fill the 
furrow. 

Fig. 119. 

The road-bed should first be properly shaped, with an 
inclination each Avay from the centre, and the timbers be 
completely imbedded in it. Two tracks should be laid, 
for the travel in the two directions. A faster vehicle, 
overtaking a slower one, could easily leave the track and 

* Pamell, p. 109. 

t See report of Mr. Jno. S. Williams, American Mechanics' Maga- 
zine, p. 210 



260 



IMPROVEMENT OF THE SURFACE. 



re-enter it after passing. The outside timber of each 
track should be smooth on its upper surface, and the 
inner one have hollowed in it a furrow, about 3 inches 
deep, 4 inches wide at bottom, and twice that at top. 
The flat timber should be wide enough to allow for the 
usual variation in the widths of vehicles. The rise of the 
road between the two timbers should just equal the depth 
of the furrow, so that the two wheels may be on the 
same level. The distance between the centres of the 
timbers should be about 5 feet ; between the two tracks a 
space of four feet should be left ; and on the outside of 
each, nine and a half feet for a summer road, making a 
total width of 33 feet, or two rods. The timber would 
be tolerably durable, being surrounded with earth on three 
sides ; and might be rendered more so by any of the 
preservatives mentioned on page 234, particularly the 
last. 



IRON TRACKWAYS. 



The wooden tracks, adopted more than two centuries ago 
in the coal-mines of England, were before long covered 
with thin plates of iron to increase their durability and to 
lessen their friction, and subsequently replaced by tracks 



entirely of iron. While a flange on 
their sides was used to keep car- 
riages upon them, they were " tram- 
roads," but when the flange ,was 
transferred from the road to the wheel, 
the trackway became a Railway. 
The extent of this topic demands for 
it a separate chapter. 



Fig. 120. 




RAIL-ROADS. 261 



CHAPTER V. 



RAIL-ROADS. 



" Nothing can do more harm to the adoption of railroads, than the 
promulgation of such nonsense as that we shall see locomotive engines 
travelling at the rate of 12, 16, 18, and 20 miles per hour!" 

Wood, on Railroads, 1825. 

" An express train on the Great Western Railway, drawing 59 tons, 
has travelled, for three hours, at the rate of 63 miles per hour !" 

Ritchie, on Railways, 1846. 

The great success and rapid extension of railroads, are 
due to that appreciation of the value of time, which is 
the characteristic of the present age. The speed obtained 
upon thenfi virtually and practically shortens distances in 
the precise ratio in vv^hich it abridges the lime occupied 
in travelling over them. 

The rapidity of motion and power of traction, which 
are attainable on railroads, depend on iheir diminution of 
friction. This is the chief element in the improvement 
of the surface of all roads, and in the preceding chapter 
we have considered, in the order of their progressive 
merits, the various means which may be employed for 
that object. In railroads we have arrived at their 
climax. 

The essential attributes of a railroad are two smooth 
surfaces, usually of iron, for the wheels to run upon. 
These surfaces must be made as narrow as possible, to 
lessen their cost, and some contrivance to keep the wheels 



262 RAIL-ROADS. 

upon them is then rendered necessary ; the usual one at 
present being a projection, or " flange," on the inner rim 
of the wheel. 

Since the peculiar wheels, which are the chief source 
of the superiority of railroads, prevent the vehicles which 
are adapted to run upon them, from being used on ordinary 
roads, railroads pass out of the practical scope of the 
present treatise ; for the details of their construction no 
longer belong to the community at large, but demand the 
highest professional skill of the Civil Engineer. The 
general interest, however, in the subject of railroads 
seems to demand some explanation of the leading princi- 
ples which should govern those engaged in their establish- 
ment, and some account of the ingenious contrivances 
which have been adopted to overcome the difficulties, 
which have, one after another, risen up in vain efforts to 
stop the progress of the giant. A brief popular view of 
these topics (without the minute practical details with 
which the subject of roads in general has been treated) 
will accordingly be given in the present chapter.* 

Wooden railways were employed as a substitute for 
common roads, in the collieries of England, soon after the 
year 1600.t The earliest record of their existence is in 
the life of the Lord Keeper North, wherein it appears that 
about the year 1670, they were used at Newcaslle-on- 
Tyne, for transporting coal from the mines to the river, 
and enabled one horse to draw four or five chaldrons. 



* The principal authorities consulted have been Lecount, " Treatise 
on Railways," from the seventh edition of the Encyclopedia Britannica ; 
Ritchie, " On Railways ;" Professor Vigvoles' Lectures ; and the reports 
and discussions in the " Civil Engineer and Architect's Journal ;" 
" Journal of the Franklin Institute ;" " American Railroad Journal," &c 

t Ritchie on Railways, p. 19. 



THEIR HISTORY. 263 

Subsequently these wooden rails were covered with plates 
of iron ; but the introduction of rails wholly of iron seems 
not to have taken place till 1767.* A projection, or 
flange, on the outer side of the rails, kept the wheels of 
carriages upon them. They were then called " Tram- 
roads." The objections to them were the broad surface 
of the plate, which collected obstructions upon it, and the 
great friction of the wheels against the side-flange. 

In 1789, was constructed the first public railway in 
England, at Loughborough, by Mr. William Jessop, and 
he introduced cast iron edge-rails, and wheels with the 
flanges cast upon them instead of on the rail, " Tram- 
roads" were, however, still in use in 1808.t 

In 1803, malleable iron rails were first tried, but not 
approved of. In 1808, they were introduced into some 
coal works in Cumberland, and used with complete suc- 
cess.| Since that time they have become almost univer- 
sal, and have been formed into a great variety of shapes, 
the best of which will be noticed in the section on " Con- 
struction." The progress from the use of horse power to 
locomotives of the present power and speed, will be in- 
cluded in the examination of " Motive powers." 

In our condensed sketch of the extensive subject of 
Railroads, divisions and subdivisions, analogous to those 
of the previously examined topic of roads in general, will 
be employed, and thus the coincidences, and the differ- 
ences, of the principles appropriate to each, will be made 
more prominent and striking. 

The following is an outline of the proposed arrange- 
ment : 



* Hornblower's Report to House of Commons in 1811. 

t Ritchie, p. 22. t R. Stevenson's Report, 1818. 



£64 RAIL-ROADS, 

I. What Railroads ought to be. 

1. AS TO THEIR DIRECTION. 

Z. AS TO THEIR GRADES. 

3. AS TO THEIR CROSS-SECTIOH. 

II. Their Location. 

III. Their Construction. 

1. FORMING THEIR ROAD-BED. 

2. THEIR SUPERSTRUOTXTRB. 

IV. Their Motive powers. 

1. HORSE POWER. 

2. STATIONARY ENGINES. 

3. LOCOMOTIVES. 

4. ATMOSPHERIC PRESSURE. 



I. What Railroads ought to be. 

To determine " What Railroads ought to be," it is first 
necessary to ascertain what are the Resistances to motion 
upon them which we must seek to overcome or diminish. 
The nature and amount of these resistances upon a 
straight and level road will be first examined, and then 
their increase on curves* and on ascents.-\' 

RESISTANCES ON A STRAIGHT AND LEVEL ROAD. 

The amount of these resistances has been usually ta- 
ken at 8 lbs. to a gross ton of 2240 lbs ; or 1 to 280 ; i. e. 
it was assumed that a weight of eight pounds suspended 
from a cord passing over a pulley, and allowed to descend 
by its own gravity, (as down a well) would draw, on a 

* See page 2*73. f See page 216. 



RESISTANCES. 265 

straight and level railroad, a car attached to the other 
end of the cord, and weighing one ton ; or that 1 pound 
would thus draw 280 lbs. But later experiments have 
shown that the resistance varies with the velocity ; that 
it is 10 lbs. per ton at a speed of 12 miles per hour, and 
over 50 lbs. at 60 miles per hour. The most satisfactory- 
analysis of it, is given by the following empirical formula, 
deduced by Mr. Scott Russell (and communicated to the 
British association in 1846) from experiments on five dif- 
ferent raihroads, mostly of the narrow gauge. 

The resistance has three principal elements ; Friction, 
Atmosphere, and Concussion. 

The first resistance is that of the Friction proper of the 
wheels and axles. It is constant at all velocities, and 
amounts, in the best-constructed carriages, to 6 lbs. per 
ton weight of train.* 

The second resistance is that of the Air. It is con- 
sidered to be proportional to the surface of the front of 
the train, and to the square of the velocity. It equals the 
weight of a column of air, whose base is the frontage of 
the train, and whose length is the height due to the ve- 
locity. This weight, for each square foot of frontage, 
and for a velocity of one mile per hour, equals 0.0027 lb., 
or jlo lb. For the usual frontage of 80 square feet, it 
is therefore one-fifth of a pound at one mile per hour. 

The third, or residual resistance, is probably due to 
the unavoidable Concussions, oscillations, flexures, im- 
bedding of wheels in rail, friction of air against sides, &c. 
It may be hereafter decomposed into various elements, 
but is now taken as proportional to the weight of the train 
and the velocity, and as being equal to J- lb. for each ton 
of train, at one mile per hour. 

* The tons here used are all grross tons of 2240 lbs. 



266 RAIL-ROADS. 

We are now prepared to find the resistance (in lbs.) of 
a straight and level railroad to the motion of a train of 
cars, whose weight (in tons), velocity (in miles per hour), 
and frontage (in square feet), are given, by the following 

RULE. 

1. Multiply the weight by 6, — for friction. 

2. Multiply the weight by the velocity, and divide by 
3, — for concussion. 

3. Square the velocity, and multiply this square by the 
frontage, and divide this product by 400, — for the at- 
mosphere. 

4. Add these three results, and the sum is the total 
resistance. Divide this by the weight, and the quotient 
is the resistance per ton. 

Example 1. A freight train of 100 tons is to be drawn 12 

miles per hour. Its frontage is 80 square feet. What is the 

resistance to be overcome by the motive force ? 

Friction = 100 X 6 =600 lbs. 

100 X 12 
Concussion = = 400 " 

12 X 12 X 80 

Atmosphere = -— = 29 " 

400 

Total resistance = 1029 lbs. 

T. . 1029 

Resistance per ton = =105- lbs. 

Example 2. A passenger train of 60 tons is to be drawn 35 

miles per hour. Its frontage is 80 square feet. Required it3 

resistance. 

Friction = 50 X 6 = 300 lbs. 

50 X 35 
Concussion = = 583 " 

35 X 35 X 80 „ . „ 

Atmosphere = = 24o " 

400 

Total resistance =1128 lbs. 

Resistance per ton = -— — = 22^ lbs. 
^ 50 2 



RESISTANCES. 



267 



Example 3. A train of 25 tons, at 60 miles per hour, would 
meet a resistance (by both theory and experiment) of 55 lbs. per 
ton. This rapid increase of resistance with velocity, is very 
striking, though it has been disputed by some experimenters. 

The above formula has been tested by Mr. Scott Rus- 
sell, and Mr. Wyndham Harding, chiefly for passenger 
trains of from 20 to 64 tons, and at speeds from 30 to 60 
miles per hour. At lower velocities, its results some- 
what exceed those of the experiments. When the rail- 
road or carriages are in bad repair, or side-M^inds prevail, 
the resistances will be greater than are here given. For 
head-winds, the velocity of the wind should be added to 
that of the train. 

The following Table shows the Resistances to Trains 
of different weights, and at different velocities, as given 
both by actual experiments and by the above formula : 
the frontage being 60 square feet. 



Velocity. 


Weight. 


Resistance 
by Exper. 


Resist, by 
Formula. 


Velocity. 


Weight. 


Resistance 
by Exper. 


Resist, by 
Formula. 


mi^ per Ar. 


tons. 


lbs. per ton. 


lbs. per ton. 


mi. per hr. 


tons. 


lbs. per ton. 


lbs. per ton. 


14 


9 


12.6 


13.9 


34 


30i 


25.0 


23.1 


16 


20i 


8.5 


13.2 


34 


18 


23.4 


27.2 


19 


40| 


8.6 


12.9 


35 


2U 


22.5 


26.1 


21 


18 


12.6 


16.7 


39 


24 


30.0 


31.0 


25 


40| 


12.6 


16.6 


47 


31f 


33.7 


33.1 


27 


40| 


12.6 


17.7 


50 


30 


32.9 


35.3 


31 


15i 


23.4 


25.4 


53 


25 


41.7 


42.1 


32 


14i 


22.5 


27.2 


61 


2U 


52.6 


54.8 



When the motive power is a Locomotive Engine, its 
own resistance must also be taken into account. The 
friction on its machinery, or working parts, may be taken 
at 7 lbs. per ton of its weight ; and its friction considered 
as a carriage at 8 lbs. per ton. To tliis should be added, 



268 RAIL-ROADS. 

according to Pambour, 1 lb. for each ton of the load drawn 
by it. Its atmospheric resistance is already taken into 
account, since, if again calculated and attributed to the 
engine, it should be deducted from the train of cars, which 
the engine in front of them shields from it. 

The usual mode of recording the resistance as so many 
lbs. " per ton," does not give a satisfactory standard of 
comparison ; one of the resistances (that of the atmo- 
sphere) being independent of the weight of the train. An 
increase of this weight (which is the divisor of the whole) 
would therefore lessen the resistance per ion, while it in- 
creased the total resistance. 

On the other hand, this atmospheric resistance no doubt 
varies somewhat with the length of the train, and the con- 
sequent increased friction of the air against the sides of 
the carriages. Dr. Lardner (in his report of 1841 to the 
British Association) considers " the resistance due to the 
air to proceed from the effect due to the entire volume of 
the train, and not to depend in any sensible degree on the 
form of the foremost car." Sharp fronts did not diminish 
it, nor did an increased frontage (as formed by boards 
projecting on each side) much increase it. Barlow, in a 
paper read before the Royal Society in 1836, considers 
the resistance of the air to increase in a ratio, not as the 
square, but, not much higher than the simple velocity. 

A new formula, which assumes this resistance to be 
directly proportional to the hulk of the train, and which 
also more minutely analyzes the resistances of the engine, 
has been deduced by Mr. D. Gooch, from experiments 
made in 1848 on a "broad gauge" road. His results 
have been much disputed. The following is an analysis 
of them : — 



RESISTANCES. 269 

For the Cars, the Frictional resistance is taken a* 6 lbs. per 
ton, as before. 

The Atmospheric resistance is assumed as equal to .he square 
of the velocity, multiplied by the bulk of the train in cubic feet, 
and that product by jos^ootj* Each ton weight of the train ia 
supposed to correspond to 180 cubic feet. The atmospheric re- 
sistance obtained by this formula would equal that given by 
Russell, in the case of a load of 55| tons. For a greater load, 
this formula makes this resistance proportionally greater than 
Russell's, and for a less load proportionally less. 

The residual or oscillatory resistance is taken at only j^ the 
product of the velocity by the weight, instead of ^, as in the 
former formula. Mr. Gooch considers this " oscillatory" re- 
sistance to be mainly the increased friction of the axle bearing 
upon its collars, in consequence of the transverse vibrations at 
high velocities, while Mr. Russell makes it include all the re- 
sistances remaining, after " friction" and " atmosphere" are de- 
ducted from the total amount. 

Example 4. Let weight of train = 100 tons ; velocity == 50 
miles per hour; required the resistance to the motion of the 
cars. 

Friction = 100 X 6 - - - - = 600 lbs. 

^ .„ . 50 X 100 

Oscillation = ~ — - - - - = 333 " 

lo 

Atmosphere = 50 X 50 X 100 X 180 X toWoit = 900 " 
Total resistance of cars ;=: 1833 lbs. 

For the Engine and tender, the resistance is separated into 
two parts. That caused by the friction of axles and machinery, 
is (in pounds per ton of their weight) equal to 5, plus one half 
the velocity in miles per hour. That due to atmosphere and load 
equals yo oVo o- of the square of the velocity multiplied by the 
weight of the train. These resistances would of course be dif 
ferent for each different engine. 



270 RAIL-ROADS. 

Example 5. With "weight of train = 100 tons ; velocity == 50 miles ; 
and Engine and tender = 50 tons, required resistance of the Engine 
and tender. 

5. + i X 50 = 30 lbs. per ton of their weight. 
TtAooX50X50X100=_1^ " 

Or, tlie total resistance of Engine and tender = 40 X 50 == 2000 lbs- 
Total resistance of Train and Engine = 1833 + 2000 = 3833 lbs., 
3833 

"'^iooT^=^^-^^^'-P''^*"°- 
The discrepancies in the results obtained by various 
experimenters and theorizers, show the great deficiencies 
which exist in the data of the experiments and in the ap- 
plication of the theoretical principles involved. 

Assuming for the present Mr. Scott Russell's formula 
to be approximately correct, we are next to examine the 
increased resistances which occur on curves, and on 
ASCENTS. This will be done under the heads of " What 
Railroads ought to be," as to their Directions, and as to 
their Grades. 



1. WHAT RAHiEOADS OUGHT TO BE AS TO THEIR DIRECTIOIT. 

Straightness of direction is much more important on 
railroads than on common roads, for two reasons ; the 
economy of straightness, and the resistances and dangers 
of curves. 



ECONOMY OF STRAIGHTNESS. 



From the great cost of the superstructure of a railroad, 
and the continually increasing expense of keeping it in re- 
pair, it is highly desirable that it should be as straight, and 
consequently as short, as possible. 

As the earthwork of a railroad costs almost nothing for 
repairs, while those of its perishable superstructure are 
very great, and proportioned to its length, as is also the 
cost, in fuel, wages, and wear and tear of the engines, 
of running the road, it will often be advantageous to 



ECONOMY OF STRAIGHTNESS. 271 

make large expenditures for the former element of cost, 
in order to lessen the length of the road, and consequently 
the annual expenditures for the latter.* 

Suppose the total cost of a railroad to be $30,000 per 
mile, the interest of which is $1800; the annual repairs 
of the superstructure $1000 per mile ; and the expenses 
of engines also $1000 per mile. The total annual ex- 
pense will then be $3800, which is the interest of $63,000, 
which sum might profitably be expended to shorten the 
road one mile, or $12 to shorten it one foot of length. If 
this single foot gained was the only result of a day's labor 
of a locating party, it would be a satisfactory equivalent 
for the expenses of such a day's work. 

On these grounds, a short route, which has the faults 
of steep grades and curves of small radius, may profitably 
receive an outlay of capital upon it, for the purpose of 
lessening these defects, equivalent to the cost of the dif- 
ference of distance between it and a longer line, which 
has better grades and curves. 

From these considerations it is also seen that a line 
ought not to diverge from the direct course between its 
extremities, and thus increase its distance, for the sake of 
the trade of a small town, for whose benefit the time and 
fare of all the passengers and freight on the whole line 
would thus be taxed. It would be preferable to make a 
branch track to the town. 

EVILS OF CURVES. 

Curves are necessary evils on most routes, enabling 
them to pass around obstacles, such as projecting hills, 
deep hollows, houses too valuable to be removed, &c. 

* See Amer. Railroad Journal, August, 1839, for an able development 
of this position, by W. B. Casey, C. E. 

18 



272 RAIL-ROADS. 

The greatest economy in curving is found when the line 
is located in a narrow and sinuous valley, with rocky 
banks, whose windings can be cheaply followed by suita 
bly adjusted curves. When the line crosses a series of 
ridges transversely, and nearly at right angles to their 
general direction, there would be little economy in lateral 
deviation and curvature. 

The evils of curves are the resistances which they offer 
to the motion of cars, and the dangers to which they ex- 
pose them. 

The following are the four principal causes of the resis- 
tances on curves :* 

1. The obHquity of the direction of themoving power; 
i. e. the angle which the line of traction, drawn from the 
engine to each car, makes with the tangent to the curve 
at the middle of each car, in the direction of which the 
cars tend to move. 

2. The pressure and consequent friction of the flanges 
of the wheels against the outer rail, due to the centrifugal 
force. 

This is partially obviated by elevating the outer rail, as 
will be hereafter explained, 

3. The pressure and consequent friction of the flanges, 
due to the parallelism of the axles ; for the directions of the 
tangents at the points of contact of each pair of wheels 
are different, and therefore if one pair of wheels be per- 
pendicular to its corresponding tangent, the other pair 
will be oblique to its tangent. 

This resistance is partly remedied by allowing a " play" 
of an inch or less between the wheels and the rails. It 
diminishes as the axles are placed nearer to each other ; 



RESISTANCES OF CURVES. 273 

and IS therefore much lessened by supporting the cars 
on two trucks, each resting on four wheels, the two axles 
of which are very near to each other. 

4. The fastening of each pair of wheels to the same 
axle, with which they turn.* The wheel on the outer 
side of a curve must revolve farther, and therefore faster, 
than the inner one, which must slide (if both are of the 
same diameter) by an amount equal to the difference 
between the lengths of the inner and outer rails of the 
curve. 

To lessen this resistance, the wheels are made conical, 
with their inner diameters greater than the outer, so that 
on curves, the outer wheels run on their greater diameter 
and the inner ones on the less. This cone may be so 
adjusted, that the wheel can run in a circle of 595 feet 
diameter without the flanges touching the rail. It was 
at first 1 in 7, but has of late been reduced to 2^0 and :^. 

Without these arrangements, the resistance of a curve 
of even a mile in radius, at a speed of 25 miles per hour, 
would equal that of an ascending grade of 9|- feet per 
mile ; and one of 700 feet radius, a grade of 77 feet, &c. 

The actual resistance has been very imperfectly ascer- 
tained. 

In the experiments of Dr. Lardner, the resistance to railway trains 
moving at ordinary speed, produced by curves of a mile radius, was 
found to be too small to be appreciable. 

It has been inferred, from experiments made on the Baltimore and 
Ohio Railroad, that a change in direction equal to an entire circle, or 
360°, produced a resistance equivalent, in its effects on the cost of 
transportation, to -^g, or nearly a quarter, of a mile in distance. 

* If they turned on the axle, as in ordinary carriages, they would 
not have sufficient steadiness to run truly at high velocities. — Lecount, 
p. 134. 



274 RAIL-ROADS. 

Another authority states that a curve of 700 feet radius, (8^°) at 
a speed of 12 miles per hour, is found in actual practice to cause a 
loss of power about equal to an acclivity of 18 feet per mile. 

Mr. Latrobe's experiments indicate that each degree of deflection 
of the curve per 100 feet, is equivalent to 1^ feet of ascent per mile ; 
e. g. a 1° curve, of 5730 feet radius, = 1^ feet grade; a 2° curve, of 
2865 feet radius, = 2i feet grade, and so on. 

The amount of mechanical power absorbed in passing 
around a curve is altogether independent of the radius of 
the curve, and depends only on the amount of the entire 
angular change in the direction of the line. When the 
curve has been run by " Angles of deflection," its length 
in chains, multiplied by its angle of deflection, equals the 
entire angular change. Thus, a curve of 1°, 30 chains 
long, off'ers the same resistance as one of 3°, 10 chains 
long.* Sharp curves are therefore not objectionable on 
the score of loss of power, though highly so from their 
wear and tear of engines and cars, displacement of rails, 
danger, &c. 

The danger of running off the track is much increased 
by curves, even of large radius, especially at high ve- 
locities. The momentum of the cars impels them onward 
in a straight line, and they are kept within the rails only 
by the flanges of the wheels and the firmness of the 
outer rail, the resistance of which gradually makes them 
follow the curvature of the road. If the momentum 
should exceed the resisting force, the cars must obey the 
former and leave the track. Curves at the foot of incli- 
nations are therefore especially objectionable, since the 
cars will come upon them with excessive velocity. The 
rocking and twisting motion thus given to the cars indi- 
cates the dangerous tendency which they thus acquire. 

* The angle of deflection of any curve may be found by dividing 5730 
by its radius in feet. 



CURVES. 275 

When sharp curves are unavoidable, they should, if 
possible, be located near stopping-places. They should 
not be placed on a steep slope, on account of the double 
resistance w^hich would then be caused to trains ascend- 
ing, and the increased danger of running off to trains rap 
idly descending. But if such location on a long slope be 
unavoidable, the grade should be flattened along the curve, 
and the difference applied to the straight portions. Curves 
should not be in deep cutting, where the impossibility of 
seeing far ahead might cause collisions, but on the parts 
in embankment, or on the surface. 

The increased velocities of the more recent railroads 
have greatly lessened the permissible smallness of the 
radii of curves. For the usual speeds employed on the 
English railways, it is recommended, that the minimum 
radius should be one mile. On the Baltimore and Ohio 
railroad, however, one of the earliest in the United States, 
there are several curves of 400 feet radius, (14|°) and one 
of 318 feet, (18°) over which locomotives pass without 
dif&culty at a speed of 15 miles per hour. 

The minimum in France, allowed by " V Administra- 
tion des Fonts et Chaussees" is 2700 feet ; or about 2°. 

The minimum curve upon the Hudson River railroad 
has a radius of 2062 feet=2f°. 

By the Parliamentary " Standing Orders" of 1846, a 
Railroad Conipany cannot diminish the radius of any 
curve to less than half a mile (2640 feet) without the 
special permission of Parliament. 



276 EFFECTS OF GRADES. 



2. WHAT RAILROADS OUGHT TO BE AS TO THEIR GRADES. 

The question of the steepest grade admissible on a 
railroad is not one of practicability, as is often supposed, 
but only one of comparative economy. Locomotive en- 
gines can be made to ascend grades of almost unlimited 
steepness, by a proportionate increase of their povsrer and 
adhesion, but their ascent becomes less and less useful in 
proportion as the grades become more and more steep. 
On an ascent of 19 feet to the mile, an engine can draw 
only about one-half its load on a level ; at 38 feet to the 
mile, only one-third, and so on, (adopting the Visual, 
though insufficient, ratio of 8 lbs. to the ton, or 1 to 280, 
as the resistance on a level) since, on this supposition, 
if the railroad rises 1 foot in 280, an additional force of 
8 lbs. will be required to draw one ton up this ascent, 
(see page 32) and therefore double the former force will be 
needed to draw the former load. Only half the load, 
therefore, could be drawn by the same force ; or that 
amount of power which could draw a load a mile on a 
level, would be exhausted in drawing it half a mile up 
this ascent.* 

* The precise ratio between the total resistance on a level road, and 
that on any ascent, and therefore between the comparative loads which 
can be carried on each, may be found by the proportion which will now 
be investigated. 

The loads on a level, and on an ascent, are in the inverse ratio of the 
resistance thereon : i. e. 

The load on the level is to the load up the ascent, as the total resist- 
ance on the ascent is to the resistance on the level. 

The resistance on the ascent is compounded of that of friction, &c. on 
the level, and that of gravity, which is such a part of the whole load, as 
the height of the ascent is of its length, as shown on page 32. 



RESISTANCES ON ASCENTS. 277 

Adopting the more correct ratio of 10^ lbs. per ton, or 
1 to 218, as the resistance at the usual freight speed of 
12 miles per hour, (see page 266) it would require an 
ascent of 24 feet per mile to double it, 48 feet to triple it, 
and so on. When the resistance is increased to 20 lbs. per 
ton, or 1 to 112, (as in the case at high velocities) an as- 
cent of 47 feet per mile is required to double it ; and a 
resistance of 30 lbs. per ton corresponds to an ascent of 
70 feet. 

These results show that heavy grades are proportion- 
ally less injurious on a road where great speed is em- 
ployed, with correspondingly great resistances, though the 
absolute loss of power caused by them remains the same. 
The late discovery, that the resistances at even slow rates 
of travel are greater than had been supposed, lessens 
greatly the objections to heavy grades, and shows them 
to be relatively much less injurious than had been imag- 
ined, seeing that so much greater an ascent is required to 
double the resistance. Besides, a small diminution in the 

Let then /= Resistance (in lbs. per ton) on a level. 

h = Ascent in feet per mile ; and---^ = Inclination. 
^ 5280 

— — - X 2240=———= Resistance per ton of Gravity. 
Oiiiiy) S3 

l4Ji 
/+.----= Total resistance on the inclination. 
•^ ^ 33 

The above proportion then becomes, 

Load on level : Load up ascent : : / -|- -^^ : /. Whence, 

T , -r 1 , . / Load on level 

Load up ascent = Load on level X — -r- = — -r • 

14A 14A 

f+W "•"33/ 

When the motive power is a Locomotive Engine, as is usual, its weight 
must be included in the " Load on level," used in the calculation, and 
finally subtracted from the resulting " Load up ascent." 

Example. — Let the weight of the cars drawn on a level, at 12 miles 
per hour, be 447 tons ; the engine 20, and the tender 14 tons : required 



278 RAIL-ROADS. 

velocity of the train would compensate for the increased 
resistance of quite a steep grade. 

The cost of draught on a railroad is nearly as the power 
employed, so that it will cost nearly twice as much to 
carry a load on a railroad with an ascending grade of 24 
feet to the mile, as to carry it on a level route. This 
consideration will therefore justify large expenditures 
upon the excavations, embankments, &c., of a railroad, 
with a view of reducing its grades. The propriety of 
such expenditures is to be determined by comparing the 
annual interest of the amount with the annual saving of 
power ever after, in drawing the expected loads over the 
flattened road. 

But, on the other hand, this principle may be carried to 
excess. These great expenses for graduation should be 
incurred only when maximum loads are to be constantly 
carried at high speeds, as on important leading lines of 
great traffic. Much steeper grades, than would be other- 
wise allowable, may be adopted on roads on which maxi- 
mum loads are not often carried, and on which the trains are 
required for public convenience to go often, and will 
therefore generally go light. The engine may be able to 
draw 400 tons on a level, and may seldom have more 
than 100 to draw. In such cases the true economy is, 

the load which the same power can draw up an ascent of 10 feet per 
mile. 

Here/= 10^, and h = 10. By the above formula, 

^ , ^ (447 + 20+14) 481 .,, , 

Lioad up ascent = — ,— • = — — rr-— - = d41.1 

2i2aO_ 1 + 0,41 

33 X lOi 

341.1— (20 + 14) = 307,1 = The load up the ascent. 

For the method of calculating the tractive power of locomotives, see 

page 325. 



EFFECTS OF GRADES. 279 

not to go to great expense in order to reduce the grades 
below such a degree of steepness as would permit the 
engmes to draw up their usual small loads ; nor to attempt 
to make a very level road, on which the engines could do 
a great deal, but would have very little to do. The 
same reasoning applies to railroads between places fur- 
nishing but a moderate amount of travel, such as the 
thinly settled parts of this country. Should the travel 
subsequently greatly increase, in an unanticipated degree, 
more frequent light trains could be sent. The enormous 
expenditures sometimes made in such situations to make 
a perfect road, have been too great for the scanty travel 
to pay interest upon, and have discouraged the proper 
construction of such as would have been really profitable. 

A great reduction of the first cost of a railroad may often 
be made, without much increasing its subsequent ex- 
penses ; inasmuch as the capital expended in the gradua- 
tion of a road has averaged, in England, fifteen times the 
cost of the locomotive power ; and as the daily cost of 
transit, due to this last, is also very small. Locomotive pow- 
er forms only about one-third of the whole working expen- 
ses of a road ; and only a part of this, say one-half, is likely 
to be affected by the grades ; so that there is only one- 
sixth of the whole w^orking expenses, which can be saved 
by making a road theoretically perfect in grades ; a small 
consideration for the interest of the extra capital, unless 
the traffic is likely to be continued, regular, and very 
heavy. 

In brief, first determine precisely what is wanted. If 
the best possible road would be justified by the import- 
ance of the traffic, make it as perfect {i. e. as straight, 
level, and unyielding) as possible, so that it can accom- 
plish the greatest amount of labor in the least time and 



280 RAIL-ROADS. 

with the smallest expenditure of power. If a cheap 
though inferior road will accommodate the traffic expect- 
ed, let such a one be made. 

In comparing two roads between the same points, one 
of which is level and the other has a summit, reached by 
an ascending grade, succeeded by a descending one, it 
must not be overlooked that there is a certain degree of 
compensating power in the descent. As to how much of 
the power lost in the ascent, is gained by the assistance 
of gravity in the descent, there is great difference of 
opinion. It was formerly supposed that on descents 
steeper than the angle of repose, 1 in 280, or 19 feet to 
the mile, the cars would be accelerated by the force of 
gravity, (which is just balanced by friction at that incli- 
nation) and that the brake would then need to be ap- 
plied, so that beyond that limit no more assistance could 
be derived from gravity. But it has been found by recent 
experiments that the resistance of the air to the motion of 
cars is far greater, and increases with the speed much 
faster, than had been imagined. This resistance, there- 
fore, opposes the accelerating tendency of gravity with a 
force increasing with the velocity, so that trains of cars 
may safely descend inclinations of 60 feet to the mile. On 
planes of 53 feet to the mile, trains have commenced 
the descent at a speed of 40 miles per hour, but instead 
of this velocity being increased, it was reduced to 30 
miles per hour. Railroads may therefore be laid out 
with grades of nearly 60 feet to the mile, with little or no 
loss of power in the descent ; and there is little practical 
loss of power in the ascent, if the loads are such as do 
not task the engines to their full power on the level por- 
tions of the road. In England it has been found that 
cheap lines with steep grades have not cost much more to 



UNDULATING RAIL-ROADS. 281 

work them than some which had cost two to three hun- 
dred thousand dollars per mile. We may therefore con- 
clude that Navier's maxim, that " The amount of power 
required to effect the transit of a line of railroad, depends 
entirely on the length of the line and the difference of 
level of its two extremities," is true, if none of the incli- 
nations upon it exceeds 60 feet to the mile, and if the 
engine is not obliged to carry its maximum load on a 
level. 

This principle of compensation on descents was carried 
to such excess a few years ago, that it was sanguinely 
recommended to make all railroads undulating, carefully 
avoiding all levels, and establishing a continual succession 
of ascents and descents. It was argued that the momen- 
tum which the cars acquired in descending one slope, 
would carry them up the next, just as a pendulum swings 
as far to the one side as to the other ; and that having 
received an impelling force at one end of the road, they 
would reach the other end, down one of these slopes and 
up the next in turn, by the assistance of gravity alone. 
Volumes have been written in attack and defence of 
this theory ; but the most fatal objection to it, even sup- 
posing the undulations all properly arranged, is, that the 
velocity which a train must have acquired when it had 
reached the foot of one slope, to be sufficient to carry it 
up the next, would be too great for safety, and that the 
irregularities of speed would be destructive to the cars 
and to the road. 



282 RAIL-ROADS. 

3. WHAT RAILROADS OUGHT TO BE AS TO THEIR CROSS. 
SECTION. 

The width of a railroad is the first element of its cross 
section to be considered, and it depends upon the width 
between the inner sides of the rails, which is called its 
" Gauge:' 

THE BROAD AND NARROW GAUGE QUESTION. 

The customary gauge is 4 feet 8| inches ; varying from 
4 "8 to 4 "9, according to the space deemed necessary for 
the play of the flanges of the wheels. This is called 
the "narrow gauge." The "broad gauge," first intro- 
duced by Mr. Brunei, on the Great Western Railway in 
England, is 7 feet. Between these two gauges is still 
going on the fiercest contest of the many which have 
arisen on the various doubtful points in the construction 
of railroads. 

The original railroads were made of the same width as 
the tram-roads, on which ran common wagons. This 
width happened to be 4 feet Si inches. The new rail- 
roads adopted the same width, for the convenience of 
using upon them the same cars, and thus this width be- 
came almost universal. Our American roads, using at 
first English engines, were necessarily formed with an 
identical gauge. Other gauges have also been employed. 
Four feet 10 inches is the New Jersey and Ohio gauge. 
Five feet is the gauge of Virginia, East Tennessee, and 
the north of Georgia. Five feet 6 inches is the gauge 
in Maine, (Atlantic and St. Lawrence Road) in Can- 
ada, (by general law) and in Missouri, (by law of 
1835). Six feet is the gauge of the Erie Railroad, and 
of its connectins; roads. 



THEIR GAUGE. 283 



ADVANTAGES OF THE BROAD GAUGE. 

The track being wider, llie cars have a broader base ; 
so that if the frost, or any other cause, raises or lowers 
one side of the road a certain amount, say one inch, it 
will cause an angular inclination of only 1 in 84 on the 
wide track, but 1 in 56^ on the narrow one. 

The breadth of base being greater, the centre of gravity, 
with equal loads, is lower ; so that there is less danger of 
the cars running off the track. They have also less lat- 
eral motion and greater steadiness, and thus add much to 
the comfort of the traveller. This steadiness may also be 
increased by placing the wheels outside of the cars. 

The broader base permits the wheels of the cars to be 
proportionally increased in size, and thus is obtained great- 
er leverage for overcoming the friction at the axles. 

Instead of letting the cars remain of the same width as 
now, in order to increase the steadiness, their width may 
be increased to correspond with that of the track, (making 
it 10 or 11 feet instead of the present 8 or 9) and then 
they will be as steady as at present, but be much more 
commodious for passengers, (giving space to sleep and 
eat) and more convenient for packing bulky freight, as 
hay, cotton, lumber, barrels, cattle on the hoof, &c. 

The preceding are the advantages belonging to the cars; 
those gained by the engines are still greater. 

The narrow track does not give width enough to make 
sufficiently large, and to arrange to the greatest advantage, 
the various parts of the engine. With their usual con- 
struction, the highest profitable speed for maximum loads 
(at the average working pressure of steam) is about 10 
miles per hour. To carry the same load at twice the 
speed, it would be necessary to double the quantity of 



284 RAIL-ROADS. 

Steam generated by the boiler, and therefore to double 
either its length or its diameter. The length of its flues 
cannot be advantageously increased ; therefore the en- 
largement must be that of its breadth. To effect this^ 
more space between the wheels is needed, and to get it, a 
wider track is required. 

Even if it be not required to carry great loads at high 
speeds, the surface of the boiler, being larger, may be 
less intensely heated, and will therefore last longer. 

As larger driving wheels may be used on the wide 
track, their adoption will enable greater speed to be at- 
tained without increasing the rate of motion of the piston. 
The expansive force of steam may therefore be employed. 

The larger and more powerful engines will do more 
work, with no more men, than smaller ones. In them 
there is therefore the same economy as in large ships. 

OBJECTIONS TO THE BROAD GAUGE. 

More ground is required ; and the excavations and em- 
bankments are wider, and therefore more expensive. 

The axles must be heavier to have the same strength as 
before. 

There is an increased resistance on the curves, in con- 
sequence of the increased sliding of the inner wheels, 
which is equal (as was seen on page 273) to the differ- 
ence betvt^een the lengths of the outer and inner rails, and 
therefore proportional to the difference of the respective 
radii of the curves. 

The larger engines of the broad gauge roads have more 
power than is generally needed, and therefore part of it is 
practically wasted. 

But on the whole, for a great road, the advantages of 
the broad gauge would indisputably overpower the objec 



THEIR GAUGE. 285 

tionsto it, if it were not for the evils of " The break of 
gauge." 

THE BREAK OF GAUGE. 

This is the name given to the interruption which occurs 
whenever a road of broad gauge meets one of narrow 
gauge, and which renders necessary the change of pas- 
sengers, baggage, and freight, from one set of cars to an- 
other, and prevents the same cars being run through without 
transhipment, or " breaking bulk." Passengers thus suffer 
much delay, confusion, and discomfort ; and merchandise 
is exposed to damage and risk of loss, in being thus changed 
from one car to another midway in its route, besides in- 
curring much unnecessary expense. The speedy convey- 
ance of troops is also an important consideration ; for 
railroads are one of the most powerful means of national 
defence, enabling an army to be concentrated rapidly at 
any point attacked ; but their value for this purppse would 
be greatly lessened if it were necessary, at some " break 
of gauge" on the route, to stop and lose the time neces- 
sary for transferring the troops, with their artillery, stores, 
&c., from one set of cars to another. 

Most roads belong to the narrow gauge class. In 
England the proportion is as 7 to 1 ; there being in op- 
eration, in 1846, 1901 miles of the narrow gauge, and only 
274 of the broad. Every new road of broad gauge, con- 
necting with a narrow one, therefore increases the evils 
of the break of gauge. The importance of lessening 
them has given rise to various contrivances for that pur- 
pose. The following are the four principal remedies pro- 
posed. 

1 . Telescopic axles. The axles have been so arranged 
that one portion slides in the other, like the joints of a 



286 RAIL-ROADS. 

telescope, so that the distance between the wheels can be 
so adjusted as to suit either the broad or the narrow gauge. 
To lessen their gauge, the catch which fastens them is 
loosened, and the carriage is pushed along a pair of rails, 
the space between which gradually narrows from 7 feet 
to 4 feet 8|- inches, and thus the wheels of the carriage 
are gradually forced nearer to each other. To widen 
their gauge the operation is reversed. But, besides the 
expense of the alteration, there is a resulting unsteadiness, 
and consequent liability to danger. 

2. Low trucks on the broad gauge roads may have rails 
laid on them 4 feet Si inches apart, upon which the nar- 
row gauge cars may be run, and thus be carried on the 
broad roads. But this contrivance raises the centre of 
gravity, making the whole top-heavy ; and adds so much 
extra dead-weight to the load. Besides, it does not provide 
for conveying the broad gauge cars on the narrow roads. 

3. Shifting car-bodies for passengers have been pro- 
vided, which could be swung, by powerful cranes, from 
one set of wheels to another ; and Moveable boxes, to re- 
ceive merchandise, have been made of such a size, that 
one should be carried on a narrow gauge track, and two 
on a broad one. 

4. Extra rails have been laid, so that the same road 
could be used for both classes of cars ; a pair of narrow 
gauge rails being laid within the broad ones, or only a 
single rail being laid, so as to be 4 feet Si inches from 
one of the broad gauge rails. But, besides the expense 
of these arrangements, there would be increased danger 
at the crossings. 

All these remedies are imperfect ; and the " break of 
gauge" seems to be an evil for which there is no cure, ex- 
cept in destroying its cause. 



THEIR GAUGE. 287 

The Royal Commission, appointed by the British Par 
iiament, in 1845, to investigate this subject, made an elab- 
orate report in 1846, and sum up as follows : 

"1. As regards the safety, accommodation, and conve 
nience of the passengers, no decided preference is due to 
either gauge ; but on the broad gauge the motion is gen- 
erally more easy at high velocities. 

" 2. In respect of speed, we consider the advantages 
are with the broad gauge ; but we think the public safety 
would be endangered in employing the greater capabili- 
ties of the broad gauge much beyond their present use, 
e-xcept on roads more consolidated, and more substan- 
tially and perfectly formed, than those of the existing 
lines. 

" 3. In the commercial case of the transport of goods, 
we believe the narrow gauge to possess the greater con- 
venience, and to be the more suited to the general traffic 
of the country. 

" 4. The broad gauge involves the greater outlay ; and 
we have not been able to discover, either in the mainten- 
ance of way, in the cost of locomotive power, or in the 
other annual expenses, any adequate reduction to compen- 
sate for the additional first cost." 

They recommend " that the gauge of four feet eight 
inches and a half, be declared by the legislature to be the 
gauge to be used in all public railways now under con- 
struction, or hereafter to be constructed, in Great Britain." 
They add, that " great commercial convenience would be 
obtained by reducing the gauge of the present broad 
gauge lines to the narrow gauge ;" and " think it desirable 
that some equitable means should be found of producing 
buch entire uniformity of gauge, or of adopting such other 

course as would admit of the narrow gauge carriage.4 

19 



288 RAIL-ROADS. 

passing, without interruption or danger, along the broad 
gauge hnes." 

The final conclusion seems to be that, if all railroads 
were now to be constructed anew, a gauge of five and a 
half, or six feet, would be considered most desirable ; but 
that the evils of a " break of gauge" are so great, in the 
present preponderance of narrow gauge roads, as to over- 
balance the disadvantages of the narrow gauge ; which 
should therefore be adopted by all future railroads which 
are to connect with others. 

WIDTH OF ROAD-BED. 

When the gauge has been decided upon, the necessary 
width of the roadway can be determined. When the road 
has a double track, the middle space between the two 
pairs of rails, for convenience and safety, should not be 
less than six feet. The side-spaces, outside of the rails, 
should, for safety, be a little more than the width of the 
track, particularly on embankments ; so that if the engine 
gets off the track, it may still remain upon the bank. This 
width also gives greater stability to the embankment and 
to the rails laid upon it, diminishing their liability to be 
disturbed by slips. These side-spaces are from 5 to 8 
feet on different railways. They should be greatest on 
roads where great velocity is adopted ; on high embank- 
ments ; and on the outside of curves. They will of 
course be less in tunnels, viaducts, bridges, &c. 

The total width of the road-bed of a railroad, with nar- 
row gauge and double track, will therefore be 6 + 2 (4|) 
-1-2x6= 27| feet. In excavations, the widths of the 
ditches on each side must be added. 

The New York and Albany Railroad is proposed to be 
26 feet wide on embankments, and 34 feet in excavations. 



THEIR WIDTH. 289 

The Massachusetts railroads are usually, for a single 
track, 15 feet wide on embankments, and 24 feet in exca- 
vations. 

If it be proposed to lay only a single track at first, and 
subsequently to add a second one, the cuttings and fillings 
should always be made at first of the full width for a 
double track ; for the extra expense of the additional width 
is but a small proportion of the whole, and a narrow cut 
or bank, is, from the want of room for the carts, &c. to 
pass, worked much more disadvantageously, and therefore 
much more expensively, than a wide one. If an embank- 
ment be subsequently widened, the new portion will not 
adhere to the side of the old one without forming the lat- 
ter into steps ; and in widening a rock excavation, a single 
blast might render the road impassable for many hours.* 

The other subjects properly belonging to the " Cross- 
section," such as the elevation of the outer rail on a curve, 
&c,, will be more advantageously examined under the 
head of " Superstructure." 

* Gen McNeill's Report on Mass. Western Railroad, 1836-7, pp. 39-44 



290 RAIL-ROADS. 

II. THE LOCATION OF RAILROADS. 

The location of railroads is guided by the same princi- 
ples as that of common roads, and made in similar man- 
ner ; but the greater importance to railroads of straight 
lines and easy grades, as has been shown in the preceding 
section, justifies and requires a much greater expenditure in 
the surveys which seek the attainment of these, and in 
the excavations, embankments, and bridges by which they 
are secured. The minor undulations of the country are 
disregarded, for they can be readily overcome by the cut- 
tings and finings which will be demanded by any traffic 
which is important enough to need a railroad for its ac- 
commodation ; and straightness is the first object : where 
a common road should go around a hill, a railroad should 
cut through it. For this reason, the compass, or some 
other angular instrument, usually takes the lead in the 
location, and is followed by the level. Upon the rough 
plot of the survey, curves are pencilled in, their centres 
and radii are determined, and then they are laid out on the 
ground, being corrected, if necessary, by calculation or 
by trial, till they pass through the desired points. The 
important calculations for excavation and embankment are 
identical with those of common roads ; but the estimate 
must include the new items of superstructure, of engines, 
cars, &c., which are to be presently examined. 

In examining the comparative merits of two rival 
routes, the relative importance of distance and grade, 
or shortness and steepness, must be determined by the 
considerations given on pages 276 — 281. To determine 
which is the least objectionable in amount of curvature, 
calculate the angular deflection of each curve, as indi- 
cated on p. 274. The sum of all of these on each line 
will be its total deflection, and the proper standard for 
comparing it with others. 



FORMING THE ROAD-BED. 291 

III. THE CONSTRUCTION OF RAILROADS. 

The two principal divisions of this part of the subject 
are — " Forming the Road-bed," (which corresponds to the 
general " Construction" of common roads) ; and the 
" Superstructure," which includes the Rails, and their 
supports, ties, &c. 

1. FORMING THE ROAD-BED. 

EXCAVATIONS. 

The Excavations on railroads are often of much greater 
depths than are ever necessary on common roads, the 
extra expense being amply repaid by the advantages of 
the easier grades and straighter lines thereby attained. 
There is an excavation (in sand) on one English railway, 
110 feet deep; and on another, 16,000,000 cubic yards 
of material were removed. The thorough drainage of 
these excavations by ditches, cross-drains, &c., is of the 
highest importance. Their sides often need to be sup- 
ported by retaining walls, in order to make steeper slopes 
possible, and thus to lessen their top width, when they 
pass through valuable ground. Sometimes these retaining 
walls are supported by iron beams, or flat arches, extend- 
ing across the railway at a sufficient height to clear the 
engines. In one remarkable cutting, 60 feet deep, the 
upper portion of it was rock, but the lower looser matter. 
If the whole cutting had been extended upwards, with 
such side slopes as the looser and lower portion required, 
it would have been more than 200 feet wide at its top, 
and would have involved very great expense in the re- 
moval of so large an amount of rock. The sides of the 
cutting were therefore made nearly perpendicular, and the 



292 RAIL-ROADS. 

loose strata at the bottom were supported by retaining 
walls, carried up till they reached the solid rock. Such 
are some of the ingenious expedients rendered necessary 
by the gigantic constructions of modern railroads. 

TUNNELS. 

The depth of an excavation frequently renders a Tunnel 
more economical. In constructing one, the centre line of 
the road must be set out with very great accuracy upon 
the surface of the ground, (by a Transit instrument) and 
" shafts" sunk at proper intervals along this line. The 
excavations are made by " headings," or " drifts," from 
shaft to shaft, and to the open ends of the tunnel. The 
material excavated is raised through these shafts, which, 
after the completion of the tunnel, serve as ventilators. 
Their distances apart should be from 500 to 1000 feet. 
If the material be earth, or stratified rock, the crown of 
the tunnel, and its sides, must be supported by a brick 
arch, and the excavation kept only a few feet in advance 
of the completed arch. 

The height of tunnels, in the clear, varies on the Eng- 
lish railways from 17 to 30 feet, and the width, for a 
double track, from 22 to 30 feet. The average sectional 
area in the clear, is 450 square feet : when an arch is 
required, the excavation would contain about 700 square 
feet. The cost per lineal foot of the English railway 
tunnels, has ranged from $30 to $150. If sufficient time 
had been allowed, they could generally have been executed 
for $60 per lineal foot. A number in England are over a 
mile in length, and one is more than a mile and three 
quarters. A gigantic one has been lately projected, which 
is to pass under the heart of London, reaching in one place 
a depth of a hundred feet beneath the surface of the ground 



EARTH WORK. 293 



EMBANKMENTS. 



The embankments of railroads demand the use of every 
possible precaution to ensure their solidity ; not only on 
account of their size, but because the vibrations imparted 
to them by the passing trains, greatly increase their ten- 
dency to slip. The expense and time required to form 
them in layers, as recommended on page 166, often forbid 
the adoption of that method. They are usually con- 
structed by raising them to their full height at one end, 
and so carrying them onward. Temporary rails are laid 
along the bank, and extended with it, and on them wagons, 
containing each about 3 cubic yards, are drawn by horses, 
or by locomotive engines, if the distance, or " lead," be 
great. 

It has been ascertained that, contrary to the usual the- 
ory and practice, the quantity of work which can be done 
on an embankment so made, and, consequently, the time 
which will be required for its completion, does not de- 
pend on the area of the face of the cutting which supplies 
it, or on the number of wagons which can be filled in it 
together ; but on their rate of speed, and on the number 
of them which can be emptied in a given time over the 
head of the embankment, to the top width of which this 
element is proportional. The number of wagons drawn 
together in a " set," should increase or decrease with the 
length of the " lead," and the breadth of the end of the 
bank ; and the number of " sets" should be increased at 
certain exact periods in the progress of the work, which 
are susceptible of mathematical determination.* 



* These points are very clearly and fully examined in " Laws of Ex- 
cavation and Embankment on Railways," London, 1840. 



294 RAIL-ROADS. 

When a railroad passes through a wooded swamp, 
where no materials for embankment are at hand, a cheap 
and efficient substitute will be formed by a series of tim- 
ber trusses. Piles of 15 inches diameter, not sharpened, 
are driven so as to form two lines, at a distance from each 
other equal to the width of the railroad. Transverse ties 
are fastened across their tops, which are braced by in- 
clined struts, the lower ends of which abut against short 
piles. Longitudinal timbers are laid on the heads of the 
piles to carry the rails. Various combinations of the 
trusses are employed, according to the height of the su- 
perstructure above the surface of the ground. After the 
railroad has been thus constructed, it may be gradually 
banked up to the level of the rails, by taking advantage 
of its facilities of transportation, to bring earth from a 
distance to the places where it is needed. 

The side-slopes of both the excavations and the em- 
bankments should be sown with grass seed, or sodded, as 
directed in the construction of roads. Some deep cut- 
tings on the English railways, have been planted with 
flowers, shrubs, and trees ; an improvement as delightful 
to the passenger and therefore profitable to the proprietors 
of the road, as it is beneficial to the permanence of the 
slopes. 



BALLASTING. 

The tops of the embankments, and the bottoms of the 
excavations, are brought to a height called the " Forma- 
tion level," about two feet below the intended level of the 
rails, and there shaped with a fall from the middle to each 
side, as in common roads, in order to drain off the water 
which falls upon them. The remaining space of tv^ro 



BRIDGES AND VIADUCTS. 295 

feet (more or less, according to circumstances) is filled up 
with "ballasting," composed of some porous material, 
such as broken stones, gravel, quarry rubbish, cinders, 
&c., through which the water of rains can readily pass. 
Upon this " ballast" are laid the supports of the rails. 
Without this precaution, the water absorbed by the earthy 
materials of the road-bed would render it soft and spongy 
in ordinary weather, and by freezing in winter would dis- 
turb the position and the levels of the rails. On many 
American railroads, the neglect of this safeguard against 
the effects of our Northern winters, renders them very 
unsafe at high velocities in the early spring, when the 
frost is coming out of the ground. Ships' ballast was 
first used fer this purpose on the early railroad at New- 
castle, and from this circumstance the substitutes have re 
tained the original name. 



BRIDGES AND VIADUCTS. 

The bridges necessary on railroads, when of stone, 
present peculiar difficulties in their construction. This is 
owing to the frequently unavoidable ^ai^we^^ of the arches, 
(a characteristic which it is not easy to unite with suffi- 
cient strength, both in reality and in appearance) and to 
the obliquity with which they often cross other roads, and 
which compels the employment of " skew-arches," which 
require more than ordinary skill in both the engineer and 
the builder. 

In this country timber bridges are the cheapest, and 
therefore almost universally employed, though faulty from 
their elasticity and consequent vibration. The leading 
plans are Col. Long's truss bridge, which has the advan- 
tage of using only timbers of small scantling, any of which 



296 RAIL-ROADS. 

can be safely taken out and replaced ; Town*s Lattice 
bridge, which is formed of planks crossing each other 
diagonally, like lattice work, and is easily constructed, 
but, though strong, is deficient in stiffness ; and Howe's 
truss bridge, in which an iron rod replaces the usual ver- 
tical posts. 

Iron bridges have been employed in Great Britain 
with great success, and their use is increasing. Cast 
iron girders, or beams, shaped thus in section, _L, are 
the simplest, and are economically used for stretches 
under 50 feet. For larger spans, separate castings are 
bolted together. Spans of 120 feet have been thus cross- 
ed. Wrought iron tie rods have been combined with 
these, but their advantages are disputed. 

Tubular girders, or hollow, box-like beams, of wrought 
iron have been very successfully introduced. They are 
cheaper and safer than any other plan for spans exceed- 
ing 50 feet. Such a bridge has been constructed over 
openings of 150 feet, the girders being 12 feet high and 
3 feet wide. 

The last stride in progress has been to make such 
sheet iron tubes large enough for railway trains to pass 
through, instead of over them. The Britannia tubular 
bridge, over the Menai straits, has two spans each of 
460 feet, and two of 250, its total length being 1500 feet. 
Its tubes are 30 feet high and 14 wide. Its top and 
bottom are cellular, being composed of two parallel 
sheets, 18 inches apart, and connected by cross plates 
which form a series of square cells or tubes. The ma- 
terial is boiler iron, from | to | inch thick, in sheets 
united by two million rivets, and stiffened by sixty-five 
miles of angle iron. Heavy trains daily cross it, with 
scarcely perceptible vibration. But its cost, $2,500,000, 
must always render it more a subject of admiration 
than of imitation. 



SUPERSTRUCTURE. 297 



2. THE StTPERSTRXTOTUEE. 



Under this head will be considered the best forms and 
weights of rails, whether supported at intervals (in chairs, 
on stone blocks or wooden cross-sleepers) or on continuous 
bearings for their whole length ; and their proper arrange - 
ment, inclination, elevation, &c., when laid. 

RAILS SUPPORTED AT INTERVALS. 

When rails are supported only at intervals, on props, 
like a bridge on piers, they are liable to be depressed be- 
tween these supports by the heavy loads which pass over 
them. It is therefore very important to give them such a 
shape as will secure the greatest strength with the least 
quantity of material. The form indicated by theory, and 
originally adopted in practice, is that called " fishbellied," 
from the rounded profile of its under side. A rail of such 

Fig. 121. 

a form, will have more power to resist deflection than a 
straight one of the same weight, in the proportion of 1 1 
to 9.* But whatever the theoretical advantages of this 
form, its inconvenience in practice, owing to its requiring 
a higher support, which is therefore less steady, has caused 
it to be generally discarded. 

The forms now used are all varieties of the parallel or 
straight rail, in which the top and bottom are parallel, 
and which has the same cross-section at all parts of 



* Lecount, p. 110. Barlow doubts this. 



298 



HAIL-ROADS. 



Fig. 122. 



its length. Usually the rail is thinner through its mid- 
dle than at its top and base. The various forms are named 
the T rail, the H rail, the hour-glass rail, &c. from the 
shape of their cross-section. The popular division of 
rails is into the " Plate rail," and the " Edge rail ;" the 
latter including all the varieties just mentioned. 

The best form of the parallel rail w^as in- 
vestigated by Professor Barlow, in behalf of 
the London and Birmingham Railway Com- 
pany, and Fig. 122 shows the section of the 
rail which he found to possess the greatest 
strength with the least material, the bottom web 
being much smaller than the head. 

Bat a double headed, or H rail, as shown 
in Fig. 123, with its top and base of the same 
size and shape, is now generally preferred in 
England. Professor Barlow considers this 
shape to be inferior in strength and conve- 
nience in fixing, its broader bearing to be of 
no advantage, and the proposed plan of turn- 
ing it over, when the upper table is worn down, to be im- 
practicable ; but still it is found preferable in practice, as 
enabling the best side to be selected, as being more easily 
keyed in its chair, and as having a broader bearing. 




Fig. 123 




Fig. 124. 



A favorite form in this country, 
sometimes called the inverted T 
rail, is shown in Fig. 124. It has 
been employed on the Boston and 
Albany railroad, and many others. 




A Compound rail, resembling a common rail slit in two lengthwise, and each half 
slioved along so as to break joints, and riveted, has been used with great success on 
the Utica and Schenectady and other railroads. 



FORM AND WEIGHT OF RAILS. 299 

The form of the rail being decided upon, its weight, on 
which its strength depends, is next to be determinedo 
The weight is expressed by the number of pounds in a 
lineal yard. Its minimum may be determined thus. A 
certain breadth is necessary for the bearing surface of the 
rail, that the wheel may run upon it without being 
grooved. 2| inches seems the minimum for this. The 
minimum breadth is desired, in order that as much as 
possible of the material may be put in the depth, the 
strength being as the simple breadth, but as the square 
of the depth. The minimum depth, to resist abrasion 
and exfoliation, is l-i- inches. This gives a sectional area 
of 21 X li inches = 3.75, or, say 4 inches, which corre- 
sponds to 36 lbs. to the yard. This is then the minimum 
weight permissible, when the rail is supported throughout 
its whole length ; but if supported at intervals it must 
have much greater weight and strength, their degree de- 
pending on the distance between its points of support. 

This distance has varied from 3 to 6 feet. It is now 
generally made less than 4 feet. For Professor Barlow's 
form of rail. Fig. 122, with a strength of 7 tons, the 
weight should be 51 lbs. per yard, for a bearing of 3 feet. 
To attain the same strength wilh a bearing of 6 feet, the 
weight should be 79 lbs. per yard. But the deflection of 
the rail with 3 tons, which in the former case is only .024 
inch, in the latter is .082 inch. Thus the longer bearings, 
when equally strong with the shorter, are much less stiff, 
and therefore much inferior to them. The effect of any 
depression under a passing load is that the engine, at 
slow speeds, after sinking into it, has an inclined plane to 
ascend, and at high speeds it leaps over the hollow, and 
strikes with great violence upon the other side of it. A 
rail having been bent half an inch, and then covered with 



300 RAIL-ROADS. 

paint, an engine with a train of cars was run over it, and 
none of the wheels touched the paint for a space of 22 
inches.* Strength to resist deflection is therefore as im- 
portant to a rail as its strength to bear weights. The 
latter should be double the mean strain or load. The 
former should not admit of a depression under a passing 
load of more than ^f o of an inch. 

The weight of rails has been yearly increasing. The 
first rails laid on the Liverpool and Manchester railway- 
were only 35 lbs. to the yard ; they have been succes- 
sively replaced by rails weighing 50, 65, and 75 lbs. to 
the yard. The rail shown in Fig. 123 weighs 75 lbs. to 
the yard, with bearings 3 feet 9 inches apart. Its whole 
depth is 5 inches ; the top and base are 2| inches ; and 
the thickness of the middle rib is about | of an inch. On 
the Massachusetts railroads the rails weigh from 56 to 60 
lbs. per yard, and rest on cross-sleepers, 2 feet 6 inches 
apart ; the weight on a driving wheel being from 5,000 to 
8,000 lbs. On the New York and Albany Railroad it is 
proposed to adopt rails of 70 lbs. to the yard, supported 
on cross-sleepers 2 feet 7 inches from centre to centre. 
A double track of such rails would require nearly 250 
tons of iron per mile. 

The rails are usually rolled in lengths of from 12 to 20 
feet. Their ends have received various shapes. Square 
or butt ends, Fig. 125, are generally 
preferred, but cause considerable 
shock to the wheel. The half-lap 
joints, Figs. 126 and 127, retain 
their positions better, but weaken the 
rail. The form shown in Fig. 128 is 

* Lecount, p. 89. 





Fig. 125. 




^ 


II 


( 


Fig. 126. 


r" 


r^ 


( 


Fig. 127. 


?_ 


> 





\ 


s\ 


•l 




— >- 




f 


// 


/ 



CHAIRS. 301 

recommended when trains run Fig. 128. 

on each track in only one di- 
rection, (as indicated by the ar- 
row) so that they never meet 
the points of the rails.* 

Between the ends of two successive lengths of rails, a 
space must be left to allow for their expansion by heat. 
The expansion of a fifteen feet rail may be taken at j}-^ 
of an inch for each degree of Fahrenheit, or } inch for 
100°. If the rails were laid in the coldest weather, a 
space of one-eighth of an inch should therefore be left 
between their ends. The force with which iron expands 
is from 6 to 9 tons per square inch of section, which cor- 
responds to 10 lbs. to the yard ; so that the rail of 70 
lbs. expands with a force of about fifty tons. 

CHAIRS. 

The rails are not fastened directly to their supports, 
but are inserted in " chairs." or pedestals, spiked to the 
blocks or cross-sleepers. The chaira are generally of 
cast iron, and weigh from 20 to 30 lbs. They are cast 
in one piece, consisting of a bottom plate, and two side 
pieces, between which the rail passes, its under surface 
being about an inch above the block. The opening of the 
chair must be as wide as the lower part of the rail, in or- 
der that it may be removed and replaced without disturb- 
ing the chair. Keys of wood, or of iron, must therefore 
be employed to fill up this opening, and to hold the rail 
firmly in the chair, but without offering any resistance to 
its longitudinal motion in expansion and contraction. 

On the Liverpool and Manchester Railway the chair, 

* Lecount, p. 113. 



302 



RAIL-ROADS. 




Fig. 130. 




Fig. 131 



shown in Fig. 129, was employ- ^'S- l^^- 

ed. The rail has on one side of 

its bottom a projecting rib which 

enters a notch in the chair, and 

another notch on the other side 

receives an iron pin. To prevent its getting loose, that 

end of the pin which enters first may be split, and opened 

when driven home. 

Another good form, shown in 
Fig. 130, was invented by Mr. 
Robert Stephenson. In it the rail 
is confined by two bolts with an- 
gular ends, which enter a small 
score in the rail, and are keyed 
home by iron keys with split ends. 

Fig. 131 represents Mr. Barlow's 
patent hollow iron key applied to 
fasten a double-headed parallel 
rail. 

Wooden keys, of similar shape, 
but solid, have been much used, owing to the great facili- 
ty which they offer of being tightened and replaced. They 
should be kiln-dried, cut, and compressed by hydraulic 
pressure, so that by their swelling, after being driven in, 
they may hold the rail very tightly. 

The chair used for the F%- 132. 

inverted T rail (of 65 
lbs.), on the Utica and 
Schenectady Railroad, is 
shown in Fig. 132, to one- 
fourth the real size. It is 
6^ inches wide, 8^ long, 21 high, and weighs 24 lbs. 

Generally the chairs are placed only at the joinings 






STONE BLOCKS. 303 

of the lengths of rails, which are fastened to the interme- 
diate supports by spikes with bent heads. 

When the supports are stone blocks, the chairs are at- 
tached to them by drilling holes in the stone, from 1| to 
2 inches in diameter, and driving into them plugs of oak. 
The chairs being properly placed over these, iron spikes 
with heads are driven through the holes in the base of the 
chair into the wooden plugs. Between the chair and the 
stone, pieces of tarred felt are placed to diminish the con- 
cussion. When the supports are of wood, the chairs are 
nailed down with strong spikes. 

STONE BLOCKS. 

Stone blocks imbedded in the ballasting, have been till 
lately the principal supports employed on the English 
railways. They are usually blocks of granite, or whin 
stone, two feet square and one foot deep. The custom- 
ary distances between their centres have been noticed on 
page 271. They are sometimes placed, as in Fig. 133, 
with their sides parallel to the line of the road ; and some- 
times diagonally, as in Fig. 134. 

Fig. 133. Fig. 134. 






TEJIHTCEnEJTZJilEr 



./^/\ /\ 



Both plans have their advocates. The former position 
offers more resistance to motion in the line of the road.* 
The latter is less stable, but is more convenient for pack- 
ing the ballast around. Circular blocks have been pro- 



* In the proportion of 1728 to 1629 For the investigation, see Lo- 
count, p. 93 

20 



304 RAIL-ROADS. 

posed in order to get equal resistance in all directions, but 
the gain would not equal the extra expense. 

The blocks must be very carefully set precisely level, 
since even a quarter inch difference in 3 feet, would 
create an inchned plane of 1 in 144, or 37 feet to the mile. 

On curves the blocks on each side of the road must be 
connected by iron tie-rods, that the exterior ones may not 
be pressed outward by the centrifugal force of the cars. 

Stone blocks have been also laid transversely, with the 
advantage of preserving the gauge of the road, but with 
the evils of great rigidity, hardness, and jolting. 

WOODEN CROSS-SLEEPERS. 

Transverse or cross-sleepers of wood are now consid- 
ered preferable to stone blocks for many reasons. They 
tie the rails together and preserve their parallelism, and 
also make the road less rigid and more elastic than the 
stone, and therefore much more smooth and pleasant to 
travellers. Thus the blacksmith puts his anvil on a block 
of wood to lessen the concussion. The only objection to 
them is their liability to decay, against which, howevei, 
there are many preservatives. 

They are usually of chesnut, oak, pitch-pine, or red 
cedar. They may be round sticks, hewn on two sides, 
so as to leave at least six inches thickness, and more if 
possible. The longer they are the better, as the extra 
length on each side of the track lessens the danger of set- 
tling. On the Massachusetts roads they are of second 
growth chesnut, 7 feet long, and 8 inches by 12. They 
are simply laid on the ballasting, except on new embank- 
ments and soft ground, in which cases they are laid on 
longitudinal timbers or sub-sills, which may be of plank 
8 inches wide and 3 or 4 thick. 



CONTINUOUS SUPPORTS. 305 

" Herron's Railroad track" is a horizontal latlice-work 
of timbers of small scantling, upon the intersections of 
which the rails rest. 

CONTINUOUS SUPPORTS. 

When rails are supported at intervals, the less the in- 
tervals and the nearer the supports, the less will be the 
yielding and deflection of the rails. Carrying out this 
principle, and continually lessening the intervals, we at 
last arrive at continuous supports. The advantages of 
such solid bearings for the rails would seem to admit of 
no dispute. It is evident that an iron bar, laid on a series 
of points, will be much more easily bent, either laterally 
or vertically, by the heavy blows or jolts of a carriage, 
than when the same bar is made to form a part of the 
solid roadway. The system of continuous supports of 
longitudinal timbers is therefore superior to any other in 
strength, solidity, and ease of motion. It has been of late 
increasing in popularity in England, in spite of the cost 
of timber in that country, while with us it has been aban- 
doned on our best roads for the system of supports at 
intervals. This has probably arisen from the circum- 
stance that most American roads with longitudinal timbers 
have been laid with plate rails, so thin that their ends 
sometimes spring up so as to form " snake-heads," and 
have thus received the scarcely caricatured description of 
" A hoop tacked to a lath." Such roads have the defects 
of instability, insecurity, inequality of surface, waste of 
power, resistance to speed, and great expense of main- 
tenance. But these faults do not belong to the system it- 
self, but to its imperfect execution. The rails should be 
heavy edge rails, of suitable form, and in contact with the 
timbers for their whole length ; and the longitudinal timbers 



306 



RAIL-ROABS. 



should be tied together by cross-sleepers. The best rail 
road in the world, the " Great Western," has such con 
tinuous bearings. The wood may be preserved from 
decay by any of the methods noticed on page 234. 
Fig. 135. 

n n a n n 



u 



n o" 



u 



TJ 



3 



In the above figure, A is the ground plan, B the side 
view, and C the end view, of such a system of railroad. 



Fig. 136. 



~) 




For these longitudinal 
bearings, chairs are un- 
necessary, and peculiarly 
shaped rails are preferable. 
A favorite form is that 
shown in Fig. 136, which 
has been made to weigh 
from 35 to 60 lbs. per yard. 
It is fastened by screws, 4 inches long, the heads of which 
are countersunk on the inner side, so as to be out of the 
way of the flange of the wheel. At the joints, four screws 
are employed. 

Sometimes the rails are fastened by spikes with bent 
heads, driven just outside of them, and clasping them 
irmly. 

The greater difficulty of packing the gravel around 



CONTINUOUS SUPPORT. 



307 




such longitudinal sleepers, and of removing and replacing 
them, is the chief cause of the general preference of cross- 
ties, or transverse sleepers. 

Triangular sleepers have Fig. 137. 

been employed, with a rail 
forked at bottom, as in the 
figure. The rail can thus 
be very firmly attached to 
the sleeper, the shape of 
which gives it much sta- ■<<<$$$; 
bility. 

Evans' method of fastening is warmly recommended by 
Professor Vignoles. The rails are rolled with a slit, or 
groove, of a dove-tailed shape, (in its cross-section) run- 
ning on their under side for their whole length. The bolts 
have heads of corresponding shape, and are slipped into 
the end of the groove, passed along it, and dropped through 
holes made at proper intervals in the longitudinal timbers. 
The lower ends of the bolts are cut into screws, and 
washers and nuts draw the rails close down to the tim- 
bers. They are easily tightened, and not exposed to in- 
jury, while spikes and screws get loose, and their heads 
are in the way. 

Upon the Great Western Railroad, between Bristol and 
London, (on which Mr. I. K. Brunei first introduced into 
England the system of longitudinal bearings) the hollow 
rail, shown in Fig. 138, was 
adopted. The original rails 
weighed only 44 lbs. to the 
yard, and were 1} inch high, 
the head of the inner screw 
being countersunk. The later ones weigh 70 lbs. to the 
yard, and are 2^ inches high ; the increase of height be- 




308 RAIL-ROADS. 

ing intended to compensate for not countersinking the nut 
of the inner screw. The longitudinal timbers are 15 by 
9 inches, and the cross-ties bolted to them at intervals of 
9 or 10 feet, are 5 by 8 inches. With such rails, and the 
broad gauge, this railroad combines speed and ease of 
motion in the highest degree yet attained. 

INCLINATION OF THE RAILS. 

The wheels having a conical shape, they would touch 
a level rail only on a narrow line, and both would soon be 
worn into grooves. To prevent this, the rails are some- 
times inclined inward, so as to meet the cone of the wheel 
more directly, and to present a broader bearing surface. 
The usual inclination is from 1 in 29 to 1 in 20. It may 
be given by sloping the blocks, or by cutting the sleepers 
which support the rails, or may be formed in the original 
rolling of the rail. An objection to this breadth of con- 
tact is that a rubbing and grinding action is constantly 
caused by the unequal velocities with which the outer and 
inner parts of the coned wheels revolve, and produces the 
same effect as if the train was dragged a certain dis- 
tance with its wheels locked. 

ELEVATION OF OUTER RAIL. 

When a railroad car enters upon a curve, the centrifur 
gal force tends to force the flanges of its wheels against 
the outer rail. To resist this tendency, the outer rail is 
made higher than the inner one, so that an inclined plane 
may be formed beneath the cars, down which they will 
tend to slide in an inward direction, in opposition to their 
centrifugal impulse. The inclination should be such that 
the two antagonist forces may just balance each other. It 
will vary with the radius of the curve, the velocity upon 



ELEVATION OF OUTER RAIL. 



309 



it, the gauge of the road, and the " cone" of the wheels. 
With these elements it may be readily calculated.* Some 
results (with the usual data) are given in the following 
table : 



RADIUS OF THE 
CURVE. 


ELEVATION OF THE OUTER RAIL. 


At 10 miles per hour. 


At 20 miles per hour. 


At 30 miles per hour. 


Feet. 


Inches. 


Inches. 


Inches. 


250 


1.14 


5.60 


12.99 


500 


0.57 


2.83 


6.56 


1000 


0.29 


1.43 


3.30 


2000 


0.15 


0.71 


1.65 


3000 


0.10 


0.47 


1.10 


4000 


0.07 


0.36 


0.83 


5000 


0.06 


0.28 


0.66 



An approximate rule for finding the elevation is this : 
" Multiply the square of the velocity, in feet per second, 
by the gauge of the railroad in inches ; and divide the 
product by the accelerating force of gravity, multiplied 
by the radius of curvature in feet, and the quotient will 
be the elevation in inches." 

For a velocity of 30 miles per hour on a curve of 1000 

leet, this rule gives - — ^^^ = 3.4 inches. 
^ 32 X 1000 

In practice the maximum of elevation is only one inch , 

which is that due to a velocity of 30 miles per hour on a 

curve of two thirds of a mile radius. When the cars go 

faster than the velocity assumed in the calculation, which 

has determined the elevation, their flanges press the outer 

rail ; when slower, they press the inner one. 

SIDINGS, CROSSINGS, ETC. 

On railroads which have only a single track, a second 
one, called a siding, is occasionally laid for a short dis- 

* See Pambour. pp. 277-290 ; and Lecount, pp. 135-140. 



310 



RAIL-ROADS. 



tance, to form a passing-place for meeting trains. CrosS' 
ings are the arrangements by which cars pass from one 
track to the other. The angle of their divergence should 
not exceed 1^° or 2° for speeds of 20 or 30 miles per 
hour, but when the speed, as in mines, is not more than 
8 miles per hour, the angle may be as many degrees.* 
They are always dangerous, and therefore the fewer of 
them that are employed the better. The misplacing of 
them, carelessly or malevolently, causes a large portion 
of the accidents on railways. Their simplest form is that 
of two " points" or " switches," which are attached at one 
end to the main track, and are moveable at the other, so 
as to continue the principal line, or to connect it at pleas- 
Fig. 139. 




ure with the side-track. The switches are usually moved 
by hand, with either a lever or an eccentric. A signal 
plate at the top of the lever, with which it moves, by its 
position shows to the engine-driver, as he approaches, to 
which track it is prepared to turn the train. Self-acting 
switches, kept in place by powerful spiral springs, and 
moved by the flanges of the engine wheels, have been 
tried ; but the system of manual operation is preferred, 
with all its uncertainties, owing to the self-acting arrange- 
ment rendering it impossible for the conductor to know 
whether the switches are in place or not until he is upon 



* Cresy, Encyclopedia of Civil Engineering, p. 1576. 



TURN-TABLES, ETC. 311 

them, when any precaution which might be required 
would be too late.* 

Turn-tables, or Turn-plates, are platforms, turning on 
rollers upon an underground circular railroad, and forming 
a very convenient substitute for switches, in transferring 
carriages from one set of rails to another. 

A Hydraulic Traversing Trame has been used instead 
of Turn-tables. It consists of a wrought-iron frame, un- 
der each corner of which is a cast-iron hydrauhc press, 
operated by force pumps. The frame is pushed under 
the carriage to be moved, the pumps are worked, and 
raise the flanges clear of the rails. The carriage is then 
moved to the desired spot and there let down.t 

SINGLE RAIL RAILROAD. 

In this arrangement a single rail is supported on posts 
at a suitable height above the ground, and passes through 
the middle of the cars, which hang from it on each side, 
like two saddle-bags on a horse. The advantages of thus 
lowering the centre of gravity are considerable ; the cars 
can never leave the track ; and the expenses of construe-, 
tion are much reduced. In some situations this system 
might be very conveniently employed. 



• Ritchie, p. 115. 

+ Cresy, Encyclopedia of Civil Engineering, p. 1282. 



312 



RAIL-ROADS. 



IV. MOTIVE POWERS. 

The principal powers which have been employed to 
move carriages on railroads are Horses, Stationary En- 
gines, Locomotives, and Atmospheric Pressure. 

1. HORSE POWER. 

The power of a horse in moving heavy loads at a slow 
rate, has been given on page 67 ; the usual conventional 
assumption being 150 lbs. moved at the rate of 2i miles 
per hour for 8 hours a day. At greater speeds his power 
very rapidly diminishes, a large portion of it being ex- 
pended in moving his own weight. The following table 
shows the results obtained by different authors ; those of 
Tredgold being for 6 hours daily labor, and those of Wood 
for 10 hours. 



VELOCITY. 


FORCE OF DRAUGHT ; ACCORDING TO 


Miles per hour. 


Leslie. 


Tredgold. 


Wood 


2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 


100 

81 

64 

49 

36 

25 

16 

9 

4 

1 




166 

125 

83 

42 


125 
83 
62 
50 
42 
36 
31 
28 
25 
23 
21 



From the above table it appears that, according to Wood, 
at 4 miles per hour a horse can draw only half his load 
at 2 miles ; at 8 miles only a quarter ; and so on. 

At 10 miles per hour Tredgold considers the power of 



MOTIVE POWERS. 313 

a horse to be 37 lbs. moved 10 miles per day. At the 
same velocity Sir John Macneill estimates it at 60 lbs,, 
moved 8 miles per day. 

The power of a horse is also very rapidly diminished 
upon an ascent. On a slope of 1 in 7 (85-°) he can carry 
up only his own weight, without any load. 

It is consequently very desirable to find a motive power 
on railroads, so much of which would not be uselessly 
lost at the high speeds which their diminution of friction 
renders possible. Steam has been therefore employed, 
through the medium of Stationary Engines, and of Loco 
motives. 

2. STATIOWAET ENGINES. 

Stationary steam engines were once the rivals of loco- 
motives, as motive powers for railroads, and were recom- 
mended by two distinguished engineers, less than twenty 
years ago, for adoption on the Liverpool and Manchester 
railway. It was proposed to place fixed engines along the 
line, at stations 1^ miles apart. These engines were to 
turn large drums, or cylinders, around which v/ere wound 
ropes, 4 or 5 inches in diameter, stretched along the road 
between the rails, and supported on rollers. The wagons 
were to be hooked to the ropes, and would be drawn on- 
wards with them, as they were wound up on the revolving 
cylinders. An endless rope might also be employed, and 
two trains of cars be drawn at the same time in opposite 

Fig. 140. 



n na-BSH-i — — — — — Q 



directions, as indicated by the arrows in the figure. When 
the cars had passed over the mile and a half, and reached 



314 RAIL-ROADS. 

the end of one rope, they could be detached from it, and 
attached to the succeeding one, without any stoppage. 

The system has some advantages for short hues over 
w^hich the travel must pass at brief intervals, ovi^ing to the 
economy of v^^orking stationary engines ; but it is utterly 
unsuited for general use. Its radical defect is, that the 
disarrangement of any single length of it, by any acci- 
dent, must stop the travel on the whole line. It is a chain, 
the failure of any link of which will render the whole use- 
less. It is therefore now seldom employed, except on 
inclined planes. 

A very convenient application of the system is, how- 
ever, seen on the London and Blackwall railway, 3|- miles 
long, with a fixed engine at each end. In this short dis- 
tance there are five intermediate stations ; but no deten- 
tion is caused by them, for a car is appropriated to each, 
in proper order — the last of the train being the one be 
longing to the first station, and so on. On reaching it, the 
sort of pincers by which the car is attached to the rope, is 
opened, and the car there stops, while the others of the 
train move on, 

A railroad worked by a stationary engine, would be the 
most convenient method of relieving the rush of travel 
through Broadway. The railroad track should be sup- 
ported on iron columns, out of the way of carriages, as in 
the figure. These columns might be placed on the edges 
of the sidewalks, where now are the lamp and awning 
posts, and by extending over the gutter they would have a 
base of 3 feet,* Their lower extremities should be set 

* This arrangement of the columns was suggested by Charles Ellett, 
Jan., C. E., in 1844, for an " Atmospheric Railroad." In 1834, Mr. J, H. 
Patten proposed to use a secondary street, and to connect the columns by 
arches across the street, forming a flooring on which horses should travel. 



STATIONARY ENGINES. 

Fig. 141 
BROADWAY RAILROAD. 



315 




in heavy masses of masonry. At top they should spread 
outward, a foot on each side, which would give sufficient 
width for the railroad track. The columns should be set 
at distances of 15 or 20 feet, and connected by flat arches. 
There would be no flooring over the street, and the rails 
would intercept no more light than do the boards which 
now connect the awning posts. No locomotives, or even 
horses, would pass over the road ; but an endless rope 
would continually run over pulleys, and hght cars would 
be under the most perfect control, and could be attached 
to it, or disengaged, at will, and stopped more easily than 
an ordinary omnibus. At the upper end of Broadway, a 
stationary engine, or the water-power of the Croton, would 
easily and cheaply keep up the circulation, which would 
pass up one side of the street and down the other. At 
each corner might be a platform, to which there would be 
a short flight of steps from the sidewalk, the ascent of 
which would be very easy ; or a certain number of corner 
houses might be used as depots, so that passengers might 
step into the cars from their second-story windows. As 



316 EAIL-ROADS. 

these cars would replace the omnibuses, the entire street 
would be left for miscellaneous travel. 

A railroad on the surface of the ground, with its con- 
tinual stream of cars stopping up the cross-streets every 
minute, would create a worse evil than that which it was 
intended to remedy ; and the endless rope could not be 
applied to it. If a railroad were made through a sec- 
ondary street, passengers would not generally leave Broad- 
way to avail themselves of it. A surface railroad being 
thus out of the question, two alternatives remain. The 
underground one will find few advocates ; and the only 
feasible arrangement seems to be the column and endless 
rope system. With its cheap construction, economical 
working, and thronged travel, it could scarcely fail to be 
the most profitable railroad ever built, and might be made 
to add largely to the city revenue. 

3. LOCOMOTIVE ENGINES. 

When a steam engine is required to move from its 
place, and to travel with its load, as do horses of flesh and 
blood, its usual weighty appendages of cold-water cistern, 
walking-beam, fly-wheel, &c., must be dispensed with. 
High-pressure steam must therefore be employed in order 
to enable the engine to combine the necessary compact- 
ness, lightness, and power. 

HISTORY. 

The first locomotive engine was constructed in 1802, 
by Richard Trevithick, who took out a patent in conjunc 
tion with Andrew Vivian.* Both were Cornwall engi- 

* In 1759, however, Dr. Robison, then a student in the University of 
Glasgow, suggested to Watt the application of the steam engine to moving 



LOCOMOTIVE ENGINES. 317 

neers. This engine was tried on common roads, but in 
1804, Trevithick applied a second one to a tram-road in 
South Wales, on which it drew ten tons of iron at the 
rate of 5 miles an hour. 

Many years elapsed before any considerable improve- 
ments were made, owing in a great degree to useless 
efforts to overcome a difficulty which never had any real 
existence. When steam is applied to propel a wheel 
carriage, each piston-rod, to which the steam gives a back- 
ward and forward motion, is attached to a pin on one of 
the wheels, called the driving-wheel, and turns it by a 
crank, as a man turns a grindstone. If there was no 
friction between the wheel and the road, the wheel would 
turn around, while the carriage would remain stationary 
But the friction, which does exist, prevents the wheel 
from slipping, and it is enabled to turn only by propelling 
the carriage forward over a distance equal to the circum- 
ference of the wheel for each complete revolution of it. 
The imaginary difficulty referred to, was the notion that 
the adhesion or " bite" between the wheel and the rail, 
was so slight that with a load, and particularly on an as- 
cent, the wheels would shp, slide, or " skid," either com- 
pletely or partially, and thus fail to propel the engine. 

Great ingenuity was expended in devising remedies for 
this non-existent evil. Wheels were at first made with 
knobs and claws to take hold of the ground ; in 1811 a 
toothed rack was laid along the road, and a wheel with 
teeth was attached to the engine and fitted into the rack ; 

wheel carriages. In 1782, Murdoch, to whom Trevithick was a pupil, 
made a model of a steam-carriage ; and in 1784 Watt described such an 
application in his patent. In 1801, Oliver Evans in Philadelphia moved a 
steam-dredging machine a mile and a half on wheels turned by its own 
engine. 



318 



RAIL-ROADS. 



and in 1812 a chain was stretched between the extreme 
ends of the road, and passed around a grooved wheel fixed 
to the engine and turned by it. But the most singular 
and ingenious contrivance was patented in 1813 by Mr. 
William Brunton. He attached to the back of his engine 
two legs, or propellers, which, being alternately moved by 
the engine, pushed it before them. The propellers imita- 
ted the legs of a man, or the fore legs of a horse, as shown 
in the figure. 

Fig. 142. 




The legs are indicated by HKF, and Hkf. H repre- 
sents the Hip-joint, K and k the Knee-joints, A and a the 
Ankle-joints, and F and/ the Feet. 

We will first examine the action of the front leg. The 
knee, K, is attached to the end of the piston-rod, which 
the steam drives backward and forward in the horizontal 
cylinder C. When the piston is driven outward, it 
presses the leg, KF, against the ground, and thus propels 
the engine forward as a man shoves a boat ahead by 
pressing with a pole against the bottom of a river. As 
tlie engine advances, the leg straightens, the point H is 



LOCOMOTIVE ENGINES 319 

.arried forward, and the extremity, M, of the 'bent lever, 
HM, is raised. A cord, MS, being attached to S, the 
shin of the leg, the motion of the lever tightens the cord, 
and finally raises the foot from the ground and prepares it 
to take a fresh step when the reversed action of the piston 
has lowered it again. 

The action of the other leg is precisely similar, but 
motion is communicated to it from the first one. Just 
above the knee of the front leg, at N, is attached a rod, 
on which is a toothed rack, R. Working in it is a cog- 
wheel, which enters also a second rack, r, below it, 
which is connected by a second rod, with a point, n, of the 
other leg. When the piston is driven out and pushes the 
engine from the knee, the rack, R, is drawn backwards 
and turns the cog-wheel, which then draws the lower rack, 
r, forwards, and operates on the hind leg, precisely as 
the piston-rod does on the front one, and thus the two legs 
take alternate steps, and walk on with the engine. 

This locomotive, or " mechanical traveller," as it was 
termed by its inventor, moved on a railway at the rate 
of 2\ miles per hour, with the tractive force of 4 
horses. 

All these contrivances were, however, rendered useless 
by the discovery in 1814, by actual experiment, that the 
adhesion, or friction, of the wheels was amply sufficient 
for propelling the engine, even with a heavy load attached 
to it, and up a considerable ascent. Even if the adhesion 
were less than it is, it could be increased to an almost un- 
limited extent, by inducing a galvanic action between the 
engine and the rails.* 

The first really successful locomotive was constructed 



* Lecount, p. 352. 
21 



320 RAIL-ROADS. 

by Mr. G'eorge Stephenson in 1814. By applying the 
" steam blast," he doubled its power and enabled it to run 
6 miles per hour, and to draw 30 tons. 

Still no great progress was made in the application of 
steam to locomotion, until, in 1829, the directors of the 
Liverpool and Manchester railway resolved to employ 
locomotives in preference to stationary engines, and offered 
a premium for the best engine, not heavier than six tons, 
which should be able to draw twenty tons at the rate of 
ten miles per hour, and should fulfil certain other condi- 
tions. Four engines appeared, but the " Rocket" engine, 
made by Mr. Robert Stephenson, won the prize, having 
run at an average speed of 15 miles per hour, and hav- 
ing performed one mile at the rate of 29|- miles per 
hour. 

Since that time the progress of improvement has been 
onward, and one engine has travelled 75 miles per hour ; 
another,* weighing ISf tons, has drawn 1268 tons 
(in a train of 158 coal-cars, 2020 feet long) 84 miles in 8 
hours, over a line of which 40 miles were level, and which 
had curves of only 700 feet radius ; and a third,* weigh- 
ing only 8 tons, has drawn 309 tons on a level, and 16 
tons up an inclined plane which rose 369 feet to the mile. 
The Rocket, however, contained the germs of all the prin- 
ciples which have been so wonderfully developed in its 
successors, and which will now be briefly noticed. 

* Made by William Norris : Philadelphia. 



LOCOMOTIVE ENGINES. 321 

PRINCIPLES. 

The power of an engine is proportional to the quantity 
of steam which it can generate in a given lime ; for each 
revolution of the wheels corresponds to a double stroke 
of each piston, and consequently to four cyhnder-fulls of 
steam. It is therefore necessary to expose the largest 
possible surface of water to the action of heat. This 
is most effectually attained by a tubular boiler, patented 
by Mr. Seguin in 1828, but perfected by Mr. Stephenson 
in 1 829. Through the boiler, which occupies the principal 
mass of the engine, run a great number of small brass 
tubes, and through them the flame and heated air pass 
from the fire-box to the chimney. The tubes are about 
6 feet long, 2 inches in diameter, and from 90 to 120 in 
number. They have been made 300 in number, and \\ 
inches in diameter.* By this contrivance, and by sur- 
rounding the fire-box with a double casing, containing 
water, all the heat is absorbed by the water before it 
reaches the chimney. 

The introduction of such tubes tripled the evaporating 
power of the engine, and caused a saving of 40 per cent 
of the fuel. But the abstraction of all the heat from the 
air, destroyed the draught of the chimney, and therefore 
the activity of the fire. This evil seemed insurmountable, 
in spite of the use of fanners, till George Stephenson 
used the waste steam, which passed from the cylinder 
after working the engine, to create an artificial draught, 
by discharging it into the chimney. This steam blast 
has been termed the life-blood of the locomotive machine. 

To economize heat still farther, the cylinders are some- 

* The tiibes being very perishable, the Earl of Dundonald and others 
have proposed to construct boilers with the water in the tubes to je heated, 
instead of the fire in the tubes. 



322 RAIL-ROADS. 

times placed within the smoke-box, or bottom of the 
chimney, so that none of their steam is condensed by the 
cold atmosphere. In this position, besides being nearer 
the centre of resistance, they act with a less injurious 
strain ; although, two pistons being necessary to pass the 
" dead-points" of the crank, their action is unavoidably 
unequal on each side in turn. But this arrangement gives 
less room for the machinery, and renders necessary a 
double-cranked axle, which is consequently much weak- 
ened, though cut from a solid mass of iron. Both 
the outside and inside arrangements have their advocates. 

Six wheels are generally employed, the two largest 
being the driving-wheels to which the power is applied. 
These are from 5 to 7 feet in diameter, the others being 
from 3 to 4. Sometimes all are made of the same size. 
Eight wheels are also used, four large and four small, the 
latter being under a truck, which supports one end of the 
engine, and is attached to it by a pivot in its centre, 
around which it can readily turn when on a curve. 
The springs are so adjusted that the principal part of the 
weight of the engine is thrown upon the driving-wheels. 
Sometimes two pairs of wheels are coupled together to 
obtain greater adhesion in ascending inclined planes, but 
this arrangement produces an unequal strain. 

The eccentrics which open and shut the slide-valves to 
admit the steam to each end of the cylinders in turn, are 
so adjusted as to shut off the steam from one end of the 
cylinder and admit it to the other a little while before the 
piston has finished its stroke, so as to permit the expan- 
sive action of steam, and to form a sort of steam spring, 
to deaden the jerks of the engine. The degree of open- 
ing of the valve in advance is termed the "lead," and 
is usually from one-eighth to one-fourth of an inch. 



LOCOMOTIVE ENGINES. 
Fig. 143. 



323 




The above figure is a longitudinal section through a 
modern locomotive engine, in one of its very varied forms. 
a represents the fire-box ; from which the flames and 
heated air pass, through the tubes h b, into the smoke-box 
at the other end of the engine. The vs^ater of the boiler, 
(which is cased with wood to prevent loss of heat by ra- 
diation) surrounds the fire-box and the tubes, and the 
steam generated by the heat thus absorbed, is collected in 
the steam chamber c. Thence it passes, through d, to the 
cylinder e, and being admitted, by the slide-valve, alter- 
nately before and behind the piston, it gives to it the re- 
ciprocating motion, which the crank on the axle of the 
driving-wheel converts into the revolution which propels 
the engine. The blast-pipe,/, conveys the waste steam 
from the cylinders into the chimney, to increase its 
draught, g g are safety-valves, one of v/hich should be 
locked up, so as to be out of the control of the engine- 
driver, h is one of the feed-pipes which conduct the 
water from the tender to the boiler, into which it is 



324 RAIL-ROADS. 

pumped by small force-pumps, which are worked by the 
engine, and the derangement of which has produced se- 
rious accidents. 

SPEED AND POWER. 

The speed of an engine depends on the rapidity with 
which its boiler can generate steam. One cylinder full 
of steam is required for each stroke of each of the pis- 
tons. Each double stroke corresponds to one revolution 
of the driving-wheels, and to the propulsion of the engine 
through a space equal to their circumference. Wheels 
seven feet in diameter pass over twenty-two feet in each 
complete revolution. To produce a speed of seventy-five 
miles per hour, they must revolve exactly five times in a 
second ; and to effect this number of revolutions each 
piston must make double that number of strokes in the 
same time. In this way does this ponderous machine 
divide time into tenths of seconds, almost as precisely as 
the delicate chronometer of the astronomer. 

This rapid reciprocating motion of the pistons is very 
destructive to the machinery, and is too great to attain the 
maximum effect of the power expended. It would there- 
fore be very desirable to lessen this rapidity, and to pro- 
vide some means of multiplying the motion of the pistons, 
as by chams on pulleys, &c. 

High velocities are also very expensive, in consequence 
of the rapidity with which the steam must be generated, 
and rammed, as it were, into the cylinders. The same 
effect might be produced by one quarter of the quantity 
of steam, if time were given it to act expansively. 

The power of an engine in drawing loads, depends on 
the pressure of the steam, which is usually kept at 50 or 
60 lbs. to the square inch. It is also limited by the adlie- 



LOCOMOTIVE ENGINES. 



325 



sion between the road and the driving-wheels, which is 
proportional to the weight pressing upon the latter ; so 
that instead of the weight of the engine being an obstacle, 
it is one of the principal elements of power. The aver- 
age adhesion may be considered to be one-eighth of the 
weight. The tractive power of an engine of 20 gross 
tons weight, with 16 tons resting on the driving-wheels, 
would, on this assumption, be 16 x 2240 -f- 8 =4480 lbs. 
If the friction be 10 lbs. to the ton, its gross load, exclu- 
sive of its own weight, would be 4480 -r- 10=448 tons. 
If the ratio of the weight of the freight to the joint weight 
of the car and freight be as 6 to 10, the quantity of freight 
which such an engine could convey on a level would be 
1% X (448 — 10) = 263 tons; the weight of the tender, 
10 tons, being deducted from the gross load. 

The diminution of this power on inclinations has been 
noticed on page 276, but is more fully shown in the fol- 
lowing Table, which is calculated for an engine of 20 tons, 
all resting on the driving-wheels, and for a friction of 8j 
lbs. to the ton. 



Ascent, in 
feet per mile. 


Tons of freight 
transported. 


Fractional part 

of tiie full load 

on a level. 


Number of engines 
necessary to trans- 
port the full load. 


Level, 


389 


1.000 


1 


10 


254 


.653 


n 


20 


185 


.476 


n 


30 


145 


.372 


n 


40 


118 


.304 


H 


50 


98 


.252 


4 


60 


84 


.215 


4| 


70 


71 


.180 


5i 


80 


63 


.160 


6^ 



326 



RAIL-ROADS. 



The friction of 8i lbs. to the ton, with which the pre- 
ceding table was calculated, was found (p. 265) to be too 
small. The following table has been calculated by taking 
the friction at 10 lbs. per ton, (the average amount for a 
slow freight speed,) the other data remaining unchanged. 
The principles of the calculation are found on pages 325 
and 276-7. The adhesion is taken at one-eighth of the 
weight resting on the driving wheels.* 



Ascent, in 
feet per mile. 


Tons of freight 
transported. 


Fractional part 

of the full load 

on a level. 


Number of engines 
necessary to trans- 
port the full load. 


Level. 


330 


1.000 


1 


10 


227 


.688 


n 


20 


170 


.51.5 


2 


30 


135 


.401 


2J 


40 


111 


.333 


3 


50 


94 


.284 


3i 


60 


80 


.242 


4 


70 


70 


.211 


4* 


80 


61 


.185 


5i 



The above table shows that, with its data, on an ascent 
of 20 feet per mile, two engines will be required to trans- 
port the load which one could draw on a level ; that three 
engines would be required on an ascent of 40 feet per 
mile, and so on. 

A comparison of the two tables also shows that by assuming 
a small amount of friction, ascents are made to appear much more 
objectionable, relatively, than if a larger amount of friction had 
been employed. Thus, on an ascent of 50 feet per mile, accord- 
ing to the former table, (calculated with the insufficient, though 
commonly assumed friction of 8| lbs. to the ton,) four engines 
are required to do the work of one upon a level ; but the latter and 
more correct table shows that only three and a half are needed. 
For higher speeds, and consequently greater resistances, the same 
ascents would be found to be relatively much less injurious, as has 
been shown, on page 34, with reference to common roads. 

* The greatest adhesion of iron upon iron is about one-sixth of the insist- 
ent weight; but in wet and freezing weather becomes almost nothing. It 
lessens with the increase of the slope of the road, nearly as the sine of the an- 
gle of inchnation. It would evidently be nothing, if the road were vertical. 



WORKING EXPENSES. 327 



WORKING EXPENSES. 



All the expenses of working the road for any given time 
are usually added together, and divided by the total num- 
ber of miles run in that time by engines drawing trains. 
In this way is obtained the common average of working 
expenses, which are thus measured by the cost of running 
trains per mile. But this principle of comparison is evi- 
dently faulty, since a train may be run for a very small 
cost per mile, but carry few passengers and little freight ; 
and thus its expenses, though small absolutely, may be 
ruinously great relatively. On the other hand, a heavy 
train may cost much more per mile, but carry so great an 
amount of freight or passengers, as to be run very cheap- 
ly, relatively to them. Fifty tons, carried for 75 cents 
per mile, would cost \\ cents per ton, while a hundred 
tons carried for even $1 per mile, would cost but 1 cent 
per ton. 

The cost of transport per mile for each passenger or ton 
of freight carried, is therefore a preferable standard, with 
certain restrictions, as affording a means of direct com- 
parison between the expenses and the receipts, which are 
the final objects of all the operations. But this, again, does 
not of itself show the comparative economy of the working 
of different roads, for a road may be worked very cheaply 
per mile run, but, having little business, at a great cost per 
passenger or per ton, since a large part of the expenses 
are the same for one passenger or for a hundred. The con- 
verse of this takes place on a heavy road, worked expen- 
sively per mile, but cheaply per passenger or ton of freiglit. 

Both these methods of comparison ought, therefore, to 
be employed in conjunction. 



328* 



RAIL-ROADS. 



The complete average expense per train per mile of run- 
ning eleven New York railroads during 1850, was 67 
cents for passenger trains, (ranging from 34 to 94 cents,) 
and 87 cents for freight trains, (ranging from 37 to 159 
cents ;) including in this the expenses of maintaining the 
road, of repairing machinery, and of operating the road. 

Upon the same roads, the average cost per passenger 
per mile was lyVo cents ; the lowest being yW, and the 
highest 2yVo • The average cost of freight per ton was 
3i-Vo cents ; the lowest being IxVo? ^^'^ the highest 4j-Vo- 
cents.* 

Upon five leading Massachusetts Railroads, the aver- 
age expenses, for Passenger trains, per mile run, was 74 
cents, (from 63 to 93 cents,) and per passenger per mile 
1 cent, (from y%\ to lyVo-) 

Upon the same five roads, the Freight expenses, per 
mile run, averaged 89 cents, (from 81 to 96 cents,) and 
per ton per mile 1 jo\ cents, (from j-^-g to 1 xVo-) 

The expenses on the Utica and Schenectady road are 
classified thus :* 



utica and Schenectady Railroad. 


Passengers 
per mile run. 


Freight 
per mile run. 




22 
21 
33 


22 
26 
94 


(Repairs and depreciation, taxes, &c.) 


(Engines, cars, tools, &c.) 


(Office expenses, Laborers, Condnctors, 
Enginemen, &c.. Fuel, Oil, and Waste, 
Damages, Superintendence, Contin- 
gencies.) 


70 


142 



• N. y. state Engineer's Report on Railroad Statistics, Jan. 7, 1851. 



WORKING EXPENSES. 



329* 



Upon the Eastern Railroad (Boston to Portsmouth, 54 
miles) the expenses were thus classified for the year end- 
ing June 30, 1850: 1,037,000 passengers, and 71,000 
tons of freight having been carried :* 



Eastern Railroad. 


Per mile run. 


Per cent. 




0.3 
12.5 
22.9 
9.9 
6.0 
8.3 
0.3 
2.3 


20 
37 
16 
10 
13 

4 


Maintenance of way 

Locomotive powur 






Mail 






62.5 


100 



With careful management in every department, trains 
carrying average loads of from 100 to 150 tons can be 
moved, on ordinary grades, at a cost of 80 cents per mile. 
Such economy of transport depends mainly, how^ever, 
upon the certainty of always carrying full loads. For this 
reason the Baltimore and Ohio Railroad carried coal, by 
contract, for 1^ cents per ton, while their ordinary traffic, 
giving the engines only half a load, cost them over 2^ cents. 
The Reading Railroad is said to be able to carry coal for 
6 mills per ton per mile, because fully loaded on the down 
trips. 

The present cost of transport on the Erie Canal is Iyuq 
cents per ton per mile, of which the State receives j^ cent, 
or nearly one-half. On the Enlarged Canal, the cost is 
estimated at 7 mills, 3 of these being tolls. f 



* Report of the President, D. A. Neal. 

+ N. Y. State Engineer's Report on Canals, Feb. 7, 1851. 



328 RAIL-ROADS. 

SAFETY OF TRAVELLING. 

The comparative safely of railroads is one of iheir 
most valuable attributes, though the one least appreciated 
and most imperfectly realized. The popular impression 
is generally the reverse of the truth, for an accident to a' 
stage-coach is seldom heard of beyond the immediate 
scene of its occurrence, while any railroad disaster is 
passed from paper to paper over the whole land. 

There are many reasons why traveling on railroads 
should be safer than on common roads. The former are 
level instead of hilly, and smooth instead of uneven ; and 
all miscellaneous travel is excluded. 

The cars are safer than coaches, because their centres 
of gravity are lower ; their axles are less exposed to vio- 
lent shocks, and therefore are less subject to break ; and 
they are altogether less exposed to be overturned. 

Locomotive engines are safer than horses, because they 
are not liable to take fright, shy, or run away : and can 
be stopped at once by a brake, tamed down by opening a 
valve, and backed by simply moving a lever. 

The statistics of railroads fully confirm the conclusions 
of theory. On the English railroads, according to the 
parliamentary returns, between 1840 and 1845, both in- 
clusive, more than 120,000,000 of passengers were car- 
ried, and of these only 66 were killed, or one in nearly 
two millions ; and only 324 others were in any way in- 
jured, or one in nearly four hundred thousand. 

On the Belgian railroads, 6,609,215 persons travelled 
between 1835 and 1839, and of these 15 were killed and 
16 wounded. But of these, 26 were persons employed 
on the railroads, and only 3 passengers were killed and 2 
wounded. In 1842, of 2,716,755 passengers, only three 



SAFETY. 329 

were killed, and of these one was a suicide, and the other 
two met their deaths by crossing the line. 

On French railroads, 212 miles in length, of 1,889,718 
passengers who travelled over 316,945 miles, in the first 
half of 1843, not one was either killed or wounded, and 
only three servants of the railroad suffered. 

Comparing with this the travelling by horse-coaches in 
the same region, we find that in seven years, from 1834 
to 1840, 74 persons were killed, and 2073 wounded ! 

But few as are the accidents on railways they are still 
much more numerous than they need be. They may be 
divided into those which arise from mismanagement and 
negligence, and those which are caused by inherent faults 
in the construction and working of the railroad. 

To the former class belong accidents from collision. 
When two engines and trains meet each other, or when 
one overtakes another, the destructive consequences, 
which so often ensue, are generally due to the careless- 
ness or ignorance of the conductors, or engine-drivers 
of the train ; and are finally attributable to the false econ- 
omy of employing at a low salary incompetent persons. 
The danger of collision would also be much lessened, if 
trains running in different directions were confined inva- 
riably to one line of rails. 

Many accidents have arisen from a slow train being 
overtaken by a faster one. There is extreme danger in 
permitting one engine to follow another, except at very 
considerable distances ; and a mile is a very short dis- 
tance when measured by the brief time in which a loco- 
motive can pass over it. 

The practice of attaching an engine behind a train to 
assist the front one in the ascent of a steep grade, is also 
fraught with danger ; for any derangement of either en- 



330 RAIL-ROADS. 

gine makes it tlie anvil on which the other one falls like a 
trip-hammer, crushmg every thing between them. 

The excessive speed demanded by the impatience of 
the travelling public diminishes the controlling power, and 
makes the consequences of any negligence or malicious 
obstruction proportionally destructive. 

Wilful disobedience of orders on the part of engine- 
drivers and conductors, (as to time, turning-out places, 
waiting for other trains, &c.) reckless exposure to possi- 
bilities of collision, and insane confidence in good-luck, 
are causes of the majority of accidents ; and though no 
faithful superintendent would permit such men to have a 
second opportunity for similar misconduct, yet the disas- 
trous effects of even the first faults might be generally 
avoided by employing only men of undoubted intelli- 
gence, experience, sobriety, and self-control, and securing 
the services of the very best of their class by liberal com- 
pensations. 

The second division of accidents included those caused 
by inherent faults in the construction and working of the 
railroad. These may be in a great degree guarded 
against, by careful and continual inspection of the line of the 
road, and examination of all parts of the engines and cars. 

The explosion of the locomotive boiler is often injuri 
ous, if not fatal, to the engine-men, and by its stoppage 
of the train may cause a collision with a fohowing one. 

The settling of an embankment may cause a depres- 
sion of one side of the road, which will compel the en- 
gine to run off. The looseness of a rail, its breakage, 
(when supported only at intervals) the misplacing of a 
switch, &c., may produce a similar result. The destruc- 
tive consequences would be much lessened, if means were 
provided for instantly detaching the train from the engine, 



SIGNALS. 331 

or if they were so coupled that they would be separated 
by any lateral strain. 

The breakage of the axles of the engine or carriages 
has caused many accidents ; but this danger is greatly 
lessened by the eight wheels of the American cars,* and 
by the appendages of " Safety-beams." 

The sparks from the locomotive chimney frequently 
communicate fire to the train, and have thus, in one in- 
stance, caused great loss of life, increased by the impos- 
sibility of communicating the intelligence to the engine- 
driver in time to arrest the disaster. 



Many of the accidents which occur with the locomotive 
system might be prevented by a uniform, simple, and 
complete plan of signals. Red flags and lights for im- 
minent danger ; green for caution ; and white for safety, 
are leading features in all the systems. The signals are 
made by the policemen, who are, or should be, stationed 
along the line, to see that the rails are clear, to communi- 
cate intelligence, to work the signals, &c. 

The Danger signal is a red flag by day, or red glass 
lamp by night, waved backwards and forwards. The en- 
gine should be stopped the moment this signal is seen. 
Any signal, violently waved, should also cause an imme- 
diate stoppage. 

The Caution signal is a green flag, or light, and should 
be obeyed by slackening the speed of the engine. When 

* In this respect we are far in advance of European Railroads, and a 
writer in the Westminster Review lately suggested, as an improvement 
of the highest importance, a peculiar style of car, which was almost pre- 
cisely identical with those which have been for many years in general 
nse on American Railroads. 



332 RAIL-ROADS. 

the green flag is held so as to point upwards, it indicates 
that another engine is less than five minutes in advance 
of the one to which the signal is made. When held 
pointing downwards, it enjoins a slow rate of speed as 
a precaution against defects in the rails at that place. 

The Safety, or " All-right" signal, is a white lamp at 
night, and by day the upright position of the policeman 
with his flags furled. 

These signals are made by the policemen, either with 
hand flags and lamps, or by arms which are moveable on 
signal posts, and worked by cords. 

In the absence of these conveniences the policeman 
makes the signal " All right," by extending his arm hori- 
zontally ; the Caution signal by holding one arm straight 
up ; and the Danger signal by holding both arms 
straight up, or by waving violently a hat, or any other 
object. 

The Danger signal is always to be made immediately 
after any engine or carriage has passed along the line, 
and is to be continued for five minutes ; it is also to be 
made whenever there is any obstruction on the line, or 
any danger of it. 

The Caution signal is always to follow the Danger 
signal, and to be continued for five minutes ; it is also to be 
made wherever there is any reason for slackening the 
speed. 

The All-right signal is to be made only when the signal- 
man has satisfied himself that the line is clear, unob- 
structed, and free from any suspicion of danger. Every 
signal-man should immediately report to his nearest 
superior officer any instance of disobedience to the signals 
which he had made. 

In foggy weather both day and night signals are given ; 



SIGNALS. 333 

and in addition, when any emergency requires the imme- 
diate and certain stoppage of any train, a detonating com- 
poundj packed in a small box, is fastened to the rail with 
slips of lead, and explodes with a tremendous noise when a 
wheel passes over it, giving an unmistakeable signal for 
instant stoppage. 

White and red lights on the front and back of a train 
at night should be so arranged and combined as to indi- 
cate the direction, speed, &c. of the train. But all these 
precautions are finally dependent for their complete suc- 
cess upon the character of the persons in the employ of 

the company. 

22 



334 EAIL-ROADS. 



4. ATMOSPHERIO FRESSITEE. 

The pressure of the atmosphere is usually assumed to 
be 15 lbs. on every square inch of surface, and though 
the equality of this pressure in all directions renders it 
generally insensible, it becomes very apparent to the 
senses when the hand is held on one end of a cylinder 
from the interior of which the air is drawn out by an 
air-pump. It is this pressure which is the motive power 
of the Atmospheric Railway. 

The first idea of such a construction seems to have 
originated in 1805, in which year an Englishman, named 
Taylor, proposed to employ atmospheric pressure for 
sending letters and parcels from town to town. His 
plan was to lay a long tube, hke a gas or water pipe, be- 
tween the places, and to fit into it an air-tight piston. If 
the air was pumped out from one end of such a tube, the 
pressure of the atmosphere would force forward the pis- 
ton, and any thing attached to it. 

In 1810, Medhurst proposed to make a tube, archwaj'', 
or tunnel, large enough to contain carriages with passen- 
gers, to be propelled in a similar manner. But this scheme 
was never put into practice, for travellers did not relish 
the idea of being shot through a tube, like pellets in a 
popgun. 

The problem was now to devise some means of com- 
municating the motion of a piston, blown through an air- 
tight tube, to a carriage on the outside of this tube, 

Medhurst, in 1827, proposed to make the desired com- 
munication and application of power, through a channel, 
or groove, on the top of the tube, filled with water to 
make it air-tight. He also suggested the use of a square 



ATMOSPHERIC POWER. 



335 



iron tube, with half its top rising and falling on hinges, 
and an arm coming through the opening to connect the 
piston to the carriage. 

Vallance, in 1824, patented a variation of the tunnel of 
Medhurst. 

Pinkus, an American residing in London, in 1834 pro- 
posed the use of a tube with a slit in its top and a sort of 
rope for the covering valve. 

But no substantial success was attained till Clegg, in 
1839, invented his flap valve, and, in conjunction with 
Samuda, developed the present system. Fig. 144 is a 

Fig. 144. 




cross-section of the pipe, valve, &c. The pipe, A, is of cast 
iron, and about eighteen inches in diameter. It is laid 
between the rails on which the carriages are to run. 
Along its top is a continuous slit, or longitudinal opening, 
through which is to pass obliquely the iron bar, or 
arm, D, which connects the piston, C, with the carriage, 
of which HH is an axle. The valve which covers this slit, 
and which is shown in cross-section at B, is essentially a 



336 



RAIL-ROADS. 



Strip of leather, one edge of which is fastened to one side 
of the sht, so that the rest of it can rise and fall, and thus 
alternately open and close the slit. In the figure it is 
represented as open. To strengthen it, plates of iron, 
each eight inches long, are attached to its upper and under 
sides. The under ones are just wide enough to fit into 
the slit ; the upper ones are a little wider, to prevent thq 
valve from being pressed into the pipe. On each side of 
the slit is a rib, or projection, cast with the pipe, and 
forming a sort of trough, at the bottom of which the valve 
lies when shut. This trough is filled with a mixture of 
tallow and bees-wax, which, after being melted and cool- 
ed, adheres to the edge of the valve and makes it perfectly 
air-tight. 

Fig. 145. 




Fig. 145 is a longitudinal section of the pipe, piston, 
and leading carriage. The same letters of reference are 
employed as in Fig. 144. 

A steam engine, at the end of a length of 3 miles of the 
pipe, works an air-pump, which draws out a portion of 
the air from the pipe, AA. The air behind the piston, 
(shown at C) being no longer balanced by the air before 
the piston, presses it forward. The small wheels, EEE, 



ATMOSPHERIC POWER, 337 

behind the piston, raise the edge of the valve in order to 
make way for the connecting arm, D, which draws the 
carriage (of which HHH are the axles) onwjtrd with the 
piston. The small wheels, FFF, behind the arm, lift 
up the valve to admit the air more freely to press on the 
back of the piston. The piston and carriage thus pro- 
ceed as long as there is a greater pressure of air behind 
than before them. 

To re-seal the valve, after the piston has passed, in 
readiness for being again exhausted, the second carriage 
of the train carries under it a small steel wheel which 
presses down the valve, and which is followed by a heater, 
or copper tube, five feet long, and filled with burning 
charcoal, which melts the composition in the trough and 
solders down the edge of the valve. 

To stop the train the brake may be applied ; or the 
lever, shown at G in Figs. 144 and 145, may open a 
valve in the piston, and admit air in front of it to destroy 
the vacuum, and consequently the propelling power. 

When the carriage has reached the end of one length 
of 3 miles, it passes into the next length of pipe by an 
entrance, or equilibrium valve, ingeniously contrived to 
permit the change without affecting the vacuum. 

The power of this system depends upon the size of the 
pipe, and the perfection of the vacuum in front of the pis- 
ton. If the pipe be 18 inches in diameter, the area of the 
piston will be 254 square inches, and if a perfect vacuum 
could be attained, the pressure of the atmosphere upon 
this surface would be 254 x 15 = 3810 lbs. CaUingthe 
friction 10 lbs. to the ton, this power would be suflicient 
to move 381 tons. In practice, however, the vacuum is 
seldom reduced below 8 lbs. to the square inch,, or half 
an atmosphere, there being an unavoidable leakage. 



338 RAIL-ROADS. 

The speed is proportioned to the rapidity with which 
the air-pump exhausts the pipe, and therefore to the ve 
locity with tvhich the air-pump piston moves, and to the 
ratio between its area and that of the travelling piston. 
Air rushes into a vacuum with a velocity of 800 miles per 
hour, and this is therefore the maximum limit of speed. 
It is probable, however, that a railroad which approxima- 
ted to this speed would find but few passengers, and a mile 
in 62 seconds, or 58 miles per hour, is the nearest ap- 
proach to it yet made. 

The vacuum may be made not only by working an air- 
pump by a steam engine or by water-wheels, but by fill- 
ing an air-tight vessel with water, subsequently allowed to 
run out at a depth greater than that at which the atmo- 
sphere will support a column of it. 

The time required to exhaust a 3 mile length of pipe, 
by the usual air-pump, is 4 minutes. Allow 5 minutes 
for the train to pass, and the 4 minutes needed to exhaust 
the pipe again, would give 9 minutes as the least possible 
interval between the starting of trains, since only one 
train at a time can be on any one length of pipe. The 
application of this system to a Broadway railway, as has 
been suggested by some projectors, would, for this reason, 
be wholly impracticable. 

The principal advantages claimed for the Atmospheric 
Railroad by its advocates are the following : 

Its cars can ascend any inclination however steep ; 
since the force capable of being applied does not depend 
at all upon the adhesion of the wheels to the rails, as in 
the case of locomotives. At a certain degree of steep- 
ness locomotive engines could not carry up themselves, 
much less a load ; while the piston of an Atmospheric 
Railroad would exert equal force if its pipe were even 



ATMOSPHERIC POWER. 339 

vertical, though of course with much less profitable 
effect. 

The engine and tender being dispensed with, the force 
which would have been expended in moving their weight 
of 20 or 30 tons, is so much clear saving. 

The rails may be made much lighter and will last much 
longer, where they have not to sustain the shocks of the 
locomotive, which is the most powerful agent in their de 
struction. 

High speed with locomotives involves great waste of 
power, in consequence of the disadvantageous velocity 
with which the pistons must move. It is not so with the 
atmospheric system. 

But greater safety is one of the most important recom- 
mendations of this system ; for the cars cannot run off 
the track, being securely attached to the pipe ; nor can 
they ever come into collision with each other, for no two 
trains can be on the same length of pipe at once. 

On the other hand, if any obstacle be on the track, 
there is less power of stopping them, and none at all of 
reversing their motions ; and the great objection to the 
stationary engine system — that the failure of one hnk de- 
ranges the whole chain — applies to this plan also. 

But the comparative economy of the Atmospheric and 
Locomotive systems is the principal element in deter- 
mining their relative merits. Much greater cheapness of 
working is claimed, by its partisans, for the atmospheric 
system, but this is strenuously denied by other engineers, 
and the testimony is so conflicting and varying, m conse- 
quence of the insufficiency of the data, that no satisfac- 
tory conclusion can be arrived at. The balance of argu- 
ment seems, however, to be against the profitable employ- 
ment of the system in ordinary cases. Under some pecu- 



340 RAIL-ROADS. 

liar circumstances, however, such as the case of a Hne 
with steep grades, on which hght trains must be run at 
short intervals, it may probably be advantageously ap- 
plied. 

The longitudinal valve being the weak point of the sys- 
tem, several attempts have been made to dispense with it. 
The most successful inventions have been those of Pil- 
brow ; and of Julien and Vallirio. 

Compressed air, Carbonic acid gas, Electro-magnetism 
&c., have been also proposed as motive powers for railroads, 
but none of them seem likely to rival, in power, speed, or 
economy, that most magnificent and life-like of all human 
creations, the Locomotive Engine. 



THE MANAGEMENT OF TOWN ROADS. 341 



CHAPTER VI. 

THE MANAGEMENT OF TOWN ROADS. 

" The money levied is more than double of what is necessary for exe- 
cuting in the completest manner the work, which is often executed in a 
very slovenly manner, and sometimes not executed at all." 

Adam Smith. 

A WISE and well-regulated system of managing the re- 
pairs of roads, and of obtaining the greatest degree of 
improvement with the least amount of labor, is as impor- 
tant as their judicious construction. The " Road-tax''' 
system, of personal service and commutation, though 
nearly universal among us, is unsound in its principle, 
unjust in its operation, wasteful in its practice, and unsat- 
isfactory in its results. Borrowed from the " statute-la- 
bor" of England, and the " Corvee'^ or " Prestation en 
nature'^ of France, like them it is a remnant of the times 
of feudal vassalage, when one of the tenures by which 
land was held was the obligation to make the roads passa- 
ble for the troops of the lord of the manor. The evil 
consequences of the system will be examined, when we 
have briefly explained its organization in the state of New 
York, where it has been rendered as perfect as its nature 
permits.* 

* A convenient edition of the revised road act, with commentaries, &c., 
was published at Rochester in 1845. 



342 THE MANAGEMENT OF TOWN ROADS. 

The directing power is vested in " Commissioners of 
Highways," who are chosen in each town at the annual 
town meeting, and have " the care and superintendence 
of the highways and bridges therein," Subordinate to 
them are " Overseers^'' of whom are chosen, at the annual 
town-meeting, as many as there are road districts in the 
town. The commissioners have the authority to direct 
the overseers as to the grade of the road, how it should be 
shaped and drained, and the like. They may also lay out 
new roads. The principal duties of the overseers are to 
summon the persons subject to perform labor on the roads, 
to see that they actually work, and to collect fines and 
commutation money. The commissioners are to estimate 
the cost of improvements necessary on the roads and 
bridges of the town, and .the board of supervisors are to 
cause the amount to be levied, but within the limit, for any 
one year, of two hundred and fifty dollars. But, if a legal 
town meeting so vote, the supervisors may levy " a sum 
of money, in addition to the sum now allowed bylaw, not 
exceeding five hundred dollars in any one year." 

" Every person owning or occupying land in the town 
m which he or she resides, and every male inhabitant 
above the age of twenty-one years, residing in the town 
where the assessment is made, shall be assessed to work 
on the public highways in suchto\yn." The lands of non- 
residents are also to be assessed. The whole number of 
days' work to be assessed shall be at least three times the 
number of taxable inhabitants in such town ; and may be 
as many as the commissioners shall think proper. 

Persons assessed to work on the highways, upon re- 
ceiving twenty-four hours' notice from the overseers, must 
appear either in person, or by able-bodied substitutes ; or 
pay a sum of one dollar for each day's neglect, unless 



DEFECTS OF THE PRESENT SYSTEM. 343 

they shall have previously commuted at the rate of sixty- 
two and a half cents per day, A team, cart, wagon, or 
plough, with a pair of horses or oxen, and a man to man- 
age them, satisfies an assessment of three days. 

Such are the principal features of the present system. 
They are all .iefective in a greater or less degree. 

In the first place, the condition of the roads, which is 
so important an element of the wealth and comfort of the 
whole community, should not be allowed to remain at the 
mercy of the indolence, or false economy, of the various 
small townships through which the roads pass. In one 
town, its public spirit, wealth, and pride, may induce it to 
make a good road ; in the adjoining town, a short-sighted 
policy, looking only to private interest in its narrowest 
sense, may have led the inhabitants to work upon the roads 
barely enough to put them into such a condition as will 
allow a wagon to be slowly drawn over them. 

In the next place, the " commissioners" who have the 
primitive direction of the improvements and repairs, 
should be liberally compensated for the time and atten- 
tion which they give to the work. Gratuitous services 
are seldom efiicient ; at best they are temporary and local, 
and dependent on the whims, continued residence, and 
life of the party ; and if the compensation be insufficient, 
the same evils exist though in a less degree. Skill, labor, 
and time cannot be obtained and secured without being 
adequately paid for. 

The third defect in the system is the annual election 
of the commissioners and overseers. When men of 
suitable ability, knowledge, and experience have been 
once obtained, they should be permanently continued in 
office. On the present system of annual rotation, as soon 
as the overseer has learned something in his year's 

9 



344 MANAGEMENT OF TOWN ROADS. 

apprenticeship, his experience is lost, and another takes his 
place, aad begins in his turn to take lessons in repairing 
roads at the expense of their condition. In other occu- 
pations, an apprenticeship of some years is thought ne 
cessary before a person is considered as qualified to prac 
tise with his .own capital ; while a road overseer, the 
moment that he is chosen, is thought fit to direct a work 
requiring much science, at the expense of the town's cap- 
ital of time, labor, and money. 

In the fourth place, the fundamental principle of the 
Road-tax is a false one. Its contemporary custom of re- 
quiring rents to be paid in kind, has long since been found 
to be less easy and equitable than money rents. Just so 
is work paid for by the piece preferable in every respect 
to compulsory labor by the day. Men are now taken from 
their peculiar occupations in which they are skilful, and 
transferred to one of which they know nothing. A good 
ploughman does not think himself necessarily competent 
to forge the coulter of his plough, or to put together its 
woodwork. He knows that it is truer economy for him to 
pay a mechanic for his services. But the laws assume 
him to be a skilful road-maker — a more difficult art than 
plough-making — and compel him to act as one ; though 
his clumsiness in repairing his plough would injure only 
himself, while his road-blunders are injurious to the whole 
community. Skill in any art is only to be acquir-ed by 
practical and successful experience, aided by the instruc- 
tions of those who already possess it. An artisan cannot 
be extemporized. 

Fifthly, labor by the day is always less profitable than 
that done by the piece, in which each man's skill and in- 
dustry receive proportionate rewards. Working on the 
roads is generally made a half holiday by those who as- 



JMEW SYSTEM PROPOSED. 345 

semble at the summons of the overseer. Few of the men 
or horses do half a day's work, the remainder of their 
time being lost in idleness, and perhaps half of even the 
actual working time being wasted by its misdirection. 

Lastly, it follows from the preceding, that the commu 
tation system operates very unfairly and severely upon 
those who commute ; for they pay the price of a full 
day's work, and their tax is therefore doubled. 

Such are the principal defects of the present system 
of managing the labor expended on town roads. But it is 
much easier to discover and to expose, than to remove them. 
In the following plan the writer has endeavored to com- 
bine the most valuable features of the various European 
systems, and to adapt them to our peculiar institutions. 

In each State, a general legislative act should establish 
all the details of construction, and determine definitely 
" What a road ought to be," in accordance with the theory 
and practice of the best engineers. Surveys should be 
made of all the leading roads, and plans and profiles of 
them prepared, so that it might be at once seen in what 
way their lines could be most efficiently and cheaply im- 
proved. 

The personal labor and commutation system should be 
entirely abolished. If the town-meeting would vote a tax 
in money oi half \he amount now levied in days' work, its 
expenditure under the supervision to be presently de- 
scribed, would produce a result superior to the present 
one. When the road is a great thoroughfare, extending 
far beyond the town, it would be unjust to levy upon it all 
the expense ; and a county tax, or, in extreme cases, a 
state appropriation, should supply what might be necessary. 

In regulating the expenditure of the money raised, the 
fundamental principle, dictated by the truest and most 



346 MANAGEMENT OF TOWN ROADS, 

far-sighted economy, should be to sacrifice a portion of 
the resources of the o'oad to ensure the good employment 
of the remainder. The justice of this principle needs no 
argument ; its best mode of application is the only diffi- 
culty. The first step should be to place the repairs of 
the roads under the charge of a professional Road-maker 
of science and experience. On his skill will depend the 
condition of the roads, more than on local circumstances 
or expenditures. His qualifications should be tested by 
a competent board of examiners, if he should not have re- 
ceived special instructions in the requisite knowledge, 
such as might well form a peculiar department of educa- 
tion in our Colleges and Normal schools. As each town 
by itself could not afli'ord to employ a competent person, 
a number of them (more or less according to their wealth 
and the importance of the roads within their bounds) 
should unite in an association for that purpose. 

The engineer thus appointed should choose, in each 
township, an active, industrious man, of ordinary educa- 
tion, to act as his deputy in making the expenditures in 
that town, and as foreman of the laborers employed during 
the season of active labor on the roads. This deputy 
might be busily and profitably employed during the en- 
tire remainder of the year, in constantly passing over in 
due rotation the whole line of rOad under his care, and 
making, himself, the slight repairs which the continual 
wear and tear of the trafiic would render necessary. If 
taken in time, he himself could perform them ; but if left 
unattended to, as is usual, till the season of general re- 
pairs, the deterioration would increase in a geometrical 
ratio, and perhaps cause an accident to a traveller, which 
would subject the town to damages tenfold the cost of 
repairs. 



NEW SYSTEM PROPOSED. 347 

The laborers hired by the deputy in each town should 
be employed by piece-work as far as is possible. This 
can be carried out to a great extent, when the superin- 
tendent is competent to measure accurately the various 
descriptions of work, and to estimate their comparative 
difficulty. When the work cannot be properly executed 
by portions allotted to one man, it may be taken by gangs 
of four or five, who should form their own associations, 
make a common bargain, and divide the pay. In work 
not susceptible of definite calculation as to quantity or 
quality, and in such only, day-labor may be resorted to 
under a continual and vigilant superintendence. 

In such a system as has been here sketched, the money- 
tax would be found to be not only more equitable than the 
personal-labor system, but even less burdensome. None 
of it would be wasted ; and those who had skill and 
strength for road-work would receive back, in wages, 
more than their share of it ; those who were skilful in 
other work might remain at that which was most profitable 
to them, and pay only their simple share of the road-tax, 
not double, as when they now commute ; and the only 
losers by the change would be the indolent, who were 
useless under- the old system, but under this, would be 
obliged to contribute their share ; while great gain in 
every way would ensue to the community at large. The 
subject urgently demands legislative attention. 



348 PLAN AND PROFILE. 




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CD / 




CO 


..msJ L J . 




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' / \ 

CO / \ 
IS / \ 

/ § \ 

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APPENDIX. 



(Referred to on Pago 117.) 



CALCULATION OF EXCAVATION AND EMBANKMENT. 



1 

r.ta- 

tion. 


2 

Distance. 


3 


4 


5 


6 


7 


8 


9 


10 i 

1 


Height 

of 

ground 

above 

daium 

line. 


Rise or fall 
for each 
diitaace. 


Height of 

grade 
above da- 
tum. 


Cut. 
+ 


Fill. 


End 
Ai'eas. 


Excavation. 
Cubic feet. 


Embankment 
Cubic feet. 


1 

2 
3 

4 
5 
6 

7 


561 

858 
825 
820 
825 
330 


46.0 
59.2 
53.9 
26.9 
0.9 
4.9 
10.0 


— 4.8 

— 7.3 

— 7.0 

— 7.0 

— 7.0 
-^9 


46.0 
41.2 
33.9 
26.9 
19.9 
12.9 
10. 




18 
20 






19 

8 






1386 

1600 



1672 

528 




388,773 

1,280,994 

660,000 


685,520 

907,500 

87,120 


4219 


36.0 


2,329,767 


1,680,140 



In the above tabular view, the first seven columns are transferred 
from page 116. The remaining columns of areas and cubical con- 
tents are filled up by the following calculations, assuming at 50 feet 
the width of road-bed ; which will be the bottom of a cutting, or 
the top of an embankment, at a height just sufficient to equalize the 
elevations and depressions of the final transverse profile of the sur- 
face of the road. The side-slopes of the excavations are supposed 
to be li to 1, and those of the embankments 2 to 1. "We are now 
prepared to take up, in turn, each of the four usual methoda of cal- 
culation. 



23 



350 



APPENDIX. 



1. CALCULATION BY AVERAGING END-AREAS. 

At Station 1 there is neither cutting nor filling. The end-area in 
column 8, opposite that station, is therefore 0. 

Fig. 14G. 
104. 




At station .2, the cross-section of the excavation is shown in the 
fxgure. Tlie " Distances out" of the side-slopes are 11 X 18 = 27 
feet. The top width is therefore 27 -f 50 + 27 = 104 feet. The 
104 -f 50 



area equals 



X 18 = 1386 ; or otherwise, since the two 



triangular portions equal a rectangle of the same base and height 
as one of them, the area = (50 + li X 18) X 18 = 1386, 

At station 3, the area equals (50 -f li X 20) X 20 = 1600. 

At station 4, the Excavation ends, or " runs out," and the area 



= 0. 



Fig. 147. 




126. 

At station 5, the section of the embankment is shaped as in the 
figure, and has an area = (50 + 2 X 19) X 19 = 1672. 

At station 6, the area = (50 -f 2 X 8) X 8 = 528. 

At station 7, the area = 0. 

The column of End-A7-eas is thus filled. 

The Cubical Contents are next to be calculated. 

The mass between stations 1 and 2, has an area of at one end, 
and of 1386 at the other, and is 561 feet long. Its contents, by the 
method which we now employ, will equal the average of the two 

areas, multiplied by the length ; i. e., ~ — X 561 = 388,773 

cubic feet. 



APPENDIX. 351 

The contents of the second mass, that between 2 and 3, equals 

1386+ 1600 

—- X 858 = 1,280,994 cubic feet. 

rr., ,- , 1600+0 , „ 

The third mass == -X 825 — 660,000 cubic feet. 

Here the excavation ends, and the embankment begins. 

m, . , 0+1672 

The fourth mass = — -^ X 820 =: 685,520 cubic feet. 

rr.. .., 1672+528 

The fifth mass =:: ■ ^ • X 825 = 907,500 cubic feet. 

r.,, . , 528 + 

The sixth mass = ^ X330 — 87,120 cubic feet. 

These results, being in cubic feet, should be divided by 27, to 
reduce them to cubic yards, the denomination in which estimates 
are made and contractors paid. This reduction would be facilitated, 
if the measuring tapes and rods were divided into yards and their 
decimal parts ; or if the distances of the stations were always 
some multiple of 54 feet. 

The results thus obtained, by averaging the end-areas, exceed 
the correct amount, as will appear from an inspection of the figure 
on the following page, from which may also be deduced the cor- 
rection to be applied. 

This figure presents a perspective view of a tapering prismoidal 
mass, such as is an excavation of unequal size at its two ex- 
tremities ; ABCD being the area of its largest end, and EFGH of 
its smallest. Conceive a plane, parallel to the base of the cutting 
CDHG, to be passed through EF. It would cut the larger end in 
the line IJ, leaving below it a quadrangular prism, with equal bases 
EFGH and CDIJ. Subdivide the remaining figure, by raising the 
vertical lines IL and JK, and passing a plane through IL and E, 
and another through JK and F. The interior body thus formed 
appears wedge-shaped, but is a triangular prism, equal to half the 
quadrangular prism, which has IJKL for base, and IE or JF for 
height. There remain two triangular pyramids, — one with base 
ALI and vertex E, and the other with base BJK and vertex F. 

The prismoid being thus dissected, the contents of the quadran^ 
gular and of the triangular prisms would be correctly obtained by 
multiplying the sum of the bases or end-areas by one-half the 



APPENDIX. 



353 



length ; but to find the contents of the pyramids, their bases should 
be multiplied by one-third of their length. The method of calcula- 
tion which we have employed multiplies the sum of the end-areas 
of the original figure, (which is composed of the prisms and pyra- 
mids which we are discussing) by one-half the length ; and there- 
fore gives a result too large by the difference between a half and a 
third — i. e., by a sixth— of the product of the bases of the pyra- 

JK X KB -ML X LA JF 
mids by their length : i. e., ^ ^ "6" ' 

Representing by d the difference of the depths of the end cut- 
tings, the ratio of the side-slopes by i- to 1, and the length of the 
cutting or filling by Z, the error in excess will be 

dU 
6 ■ 



d X sd ■{■ d X sd I _. 
2 ^"6- 



If this be calculated for each mass, and subtracted from the results 

previously obtained by averaging end-areas, the remainder will 

equal the result obtained by the correct prismoidal formula, to be 

hereafter examined. Thus, for the mass between stations 1 and 2, 

14 X 18= X 561 

the correction is =45,441, — givuig a remamder 

b 

= 388,773 — 45,441 = 343,332, which is the correct amount. The 

original and corrected amounts are presented below in a tabular 

form : 



1 ORlGINAli AMOUNT.^. 


COFRECIIONi. 


CORRECTED AMOUNTS. 


Excavation. Embankment 


Formula. 


Amounts. 


Excavation. 


Embankment. 


388,773 

1,280,994 

660,000 


685,520 

907,500 

87,120 


14X182X561 


45,441 

858 

82,500 


98,673 

33,275 

7,040 


343,332 

1,280,136 

577,500 


586,847 
874,225 
80,080 


6 

liX 22X858 


6 
1^X202X825 


6 

2 X192X820 


6 
2 X112X825 


6 
2 X 82x330 


6 


2,329,767 


1,680,140 


128,799 


138,988 


2,200,968 


1,541,152 



We thus see that the method of calculating excavation and em- 
bankment by averaging the end-areas, though very generally used, 



354 



APPENDIX. 



is so incorrect that in the present example its excess over the truth 
is nearly 130,000 cubic feet in the excavation, and 140,000 in the 
embankment, or 270,000 in the whole, equal to 10,000 cubic yards. 
If this method had been used in estimating the payment due to a 
contractor at 10 cents per yard, he would have been consequently 
overpaid $1000. 

2. CALCULATION BY THE MIDDLE AREAS. 

The second method of calculation is to deduce the middle area 
of each prismoidal mass from the middle height, or arithmetical mean 
of the extreme heights, and multiply it by the length. 

Applying tkis method to the preceding example, and adopting the 
columns 1, 2, 6, and 7 of the table on page 116, we obtain the re- 
sults exhibited in the last three columns of the following table. 



Station. 


Distance. 


Cut. 


,,.,, Middle 
'^^'"- Heigiits. 


Middle 
Areas. 


Excavation. 


Embankment. 


1 







9 


571.5 


320,611 




2 


561 


18. 


19 


1491.5 


1,279,707 




3 


858 


20. 




10 


650. 


536,250 




4 


825 








9.5 


655.5 




537,510 


5 


820 




19. 


13.5 


1039.5 




857,587 


6 


825 




8. 


4 


232. 




76,560 


7 


330 




0. 1 












2,136,568 


1,471,657 



The following formula show the method of obtaining the " mid- 
dle areas" in the sixth column of the above table. 
Middle height = 9. Middle area = (50+l|X 9) X 9 = 571.5 
" =(50+1^X19) X19 =1491.5 
" =(50-|-UX10) XIO =650. 
" =(50+2X 9.5)X9.5 = 655.5 
" = (50+2X13. 5)X 13.5=1039.5 
» = (50-f2X4) X4 = 232. 
The cubical contents are then calculated as follows : 
571.5X561= 320,611.5 cubic feet. 
1491.5 X 858 = 1,279,707. " " 
650. X 825 = 536,250. " " 
655.5 X 820 = 537,510. " " 
1039.5 X 825 = 857.587.5 " " 
232. X330= 76,560. " " 





= 19. 




= 10. 




= 9.5 




= 13.5 




= 4. 



APPENDIX. 355 

The results thus obtained are too small ; their deficiency being 

equal to just half the excess of the first rasthod. This will appear 

by again referring to the figure on page 352. It will be seen that 

the contents of the prisms in that figure will be correctly given by 

this method, but that the deficiency is in the pyramids. Calling 

d . d 

'heir middle heights - ; their middle widths will be 5 — ; their mid- 

^' , d^ 

"lie areas s -x ; the contents of one of them si -5 ; and of the two 

o O 

, rf- „ , ^ , . , . /dXsd l\ 

u - . but the true contents of the pyrarnids is 2 fl — - — X - I 

d"' 
= 5Z — ; and the deficiency of the method of middle areas is 

•herefore the difl:erence between a third and a fourth — i. e. a twelfth 
— of the product of the bases of the pyramids by their length, or 

■ — ■ . Corrections thus calculated, and added to the above results, 
12 ' 

would make them coincide with the true ones given by the pris- 

moidal formula, which we will next consider. 

3. CALCULATION BY THE PRISMOIDAL FOEMULA. 

The mass, of which the volume is demanded, is a true Prismoid, 
and its correct contents will therefore be given by the well-known 
prismoidal formula, which is as follows : 

Find the area of each end of the mass, and also the middle area 
corresponding to the arithmetical mean of the heights of the two 
ends. Add together the area of each end, and four times the 
middle area. Multiply the sum by the length, and divide the pro- 
duct by 6. The quotient will be the true cubic contents required. 

Applying this method to the original example, and adopting col- 
umns 1, 2, 6, 7, 8, from page 349, and the middle areas from page 
354, we may prepare the following table : 



356 



APPENDIX. 



Station. 

1 

2 
3 

4 
5 

6 

7 


Distance. 


Cut. 


Fill. 


End 
Areas. 


Middle 
Areas. 


Excavation. 


Embankment. 


561 

858 
825 
820 
825 
330 




18 

20 





19 

8 




1386 
1600 



1672 

528 




571.5 
1491.5 

650. 

655.5 
1039.5 

232. 


343,332 

1,280,136 

577,500 


586,847 

874,225 

80,080 


2,200,968 
1,541,152 

059,816 


1,541,152 



The manner of obtaining the amounts in the last two columns is 

as follows : 

561 
• (0 + 1386 + 571.5 X 4) X — - = 343,332. 

o 

858 
(1386 + 1600 + 1491.5 X 4) X -^ = 1,280,130. 

b 



(1600+ 0+ 650 



, 825 
X 4) X — - = 577,500. 

D 

820 
(0 + 1672 + 655.5 X 4) X -^- = 586,847. 
o 

(1672 + 528 + 1039.5 x 4) X -^ = 874,225. 

b 



(528 + 0+232 X 4) X 



330 



= 80,080. 



Whatever the shape of the raass of earth intercepted between 
two parallel cross-sections, it may be divided into prisms, pyramids, 
wedges, or frustra of pyramids, to all which, and therefore to the 
entire m.ass, the prismoidal formula may be correctly applied.* 

The labor of the calculation may be much lessened by the use 
of tables, such as those of Macneill, Bidder, Fourier, Johnson, &c. 
A specimen of Macneill's is given at the end of the volume. 

The prismoidal formula may be readily deduced from the dis- 
sected figure on page 352. Call the height of the lesser end h ; of 
the greater end g ; the breadth of base b ; the ratio of the side- 
slopes to unity s; and the length I. Then we may proceed thus: 



* Journal of the Franklin Institute, January and June, 1840 



APPENDIX. 357 

Area of the smaller end EFGH = hib-{- sh) — hh + sh\ 

.•. Content of the lower prism = {bh + sh^) X I, . . . [A] 

Area of rectangle IJKL =: {b -\- 2sh) (g — h) = 5^ + 2sgh 

— bh — 2sh\ 

I 
.'. Content of the upper prism == (J)g-^2sgh — bh — 2sh'^)X-, [B] 

Bases of the two pyramids = {g — h) X s (g — h) = sg' — 
2sgh + sh\ 

.•. Contents of the pyramids (5^^^ — 2sgh ■{- sh!') X -r, . . [C] 

Uniting the expressions for the partial contents [A], [B], and 
[C], and reducing them to a common denominator, we get for the 
contents of the prismoid, 

(65/i +65A'+ 3bg+ 6sgh — 2bh — Gsh'' + 2sg'' — Asgh + 2sh?) X ^ 

= {2bh + Ug + 2sgh-\-2sg''+2sh'') X - [D]. 

This expression may be decomposed into the following : 
{bh + sh' + bg-\- sg-" + 2bg + 2bh + 2sgh + sg-" + sK^) X ^. 

D 

The first two terms express the area of the smaller end of the 
prismoid, and the next two the area of the larger end. The re- 
maining five terms may be transformed into 

which is the expression for 4 times the middle area ; thus giving 
the prismoidal formula. 

The formula [D], giving the contents of the prismoid, may be 
transformed into another, more convenient for calculation than the 
usual prismoidal one. By separation into factors, it becomes, 

[2s{gh-Vg'' + h')-VZbQi + g)\X^ [E] 

■which gives the following 



Add together the squares of the heights at each end, and their 
product. Multiply the sum by twice the ratio of the side-slopes to 
unity Reserve the product. Multiply the sum of the heights by 



358 APPENDIX. 

three times the breadth of base, and add the product to the reseryed 
product. Multiply their sum by the length or distance between the 
two cross-sections, and divide by six. 

Applying the rule to the mass between stations 2 and 3, we find 
^ = 20, A = 18, b =■ 50, 5 = 1|, ^ = 858, and the calculation is 
made thus : 

18^ = 324 

20' = 400 

18 X 20 = 360 

1084 X 2 X IJ^ = 3253 





18 








20 








38 X3 X 


50 


= 5700 

8952 






6)' 


858 




7680816 


Cubical contents = 




1280136 



Formula [E] may be also transformed into the following formulce, 
either of "which is more convenient for calculation than the usual 
prismoidal formula. 

[2s (g — hr +3b(g+h)+ 6sgh] X~ . . . [F] 

D 

or [25 (a- -f hr +3big+ h) — 2sgh-\ xj. . . [G] 

b 

WheJi the side-slopes are \\ to 1, the preceding formulae are 
much simplified, for 25 = 3, and the factor three may therefore be 
eliminated from each term, and one-half, instead of one-sixth, of 
the length be used as a multiplier. 

Formula [G] then becomes 

[(g+hr-hi{g + h)-gh]x^^ 

^[ib + g + h)(g+h)-gh]X^. . . [H] 
This formula gives the following 



APPENDIX. 359 

RULE. 

When the side-slopes are 1^ to 1, add together the breadth of 
base and the heights at each end of the mass. Multiply this sum 
by the sum of the two heights. From the product subtract the pro- 
duct of the two heights. Multiply the remainder by half the length. 

The calculation of the preceding example will then be made thus : 

50 

18 18 
20 20 

88 X 38=: 3344 
18 X 20= 3G0 

2984 
858 -^ 2= 429 

Cubical contents = 1,280,136 

When the height and therefore area at one end = 0, h vanishes 
from the formula [E], which thus becomes 

(250-^ -h 3bg) X i = (250- + 3W ^ [I] 

giving the following 

RULE. 

Add the product of the height by twice the slope to three times 
the breadth of base. Multiply the sum by the height, and that pro- 
duct by the length, and divide the product by six. 

The calculation of the cubical contents of the mass between sta- 
tions 1 and 2 will accordingly be thus made : 

2X 1|X 18= 54 

3 X 50 = 150 18 X 661 

204 X = 843332. 

o 

204 

When these last two conditions are combined (i. e. slopes l^- to 1, 
and one height = 0) formula [I] becomes, still more simply, 

n-^ [■'] 



360 APPENDIX. 



FORMULA FOR A SERIES OF EO.UAL DISTANCES. 

When the cross-sections have been taken at uniform distances 
apart, (as is usual in the final location of a Road or Railroad, one 
hundred feet being the customary interval) the calculation of the 
cubical contents of the successive prismoids may be reduced to a 
single operation for the whole series, and therefore much short- 
ened, by the use of the symmetrical formula which will be now 
investigated, and presented in the form of a Rule. 

Through the first prismoidal mass of earth, conceive two verti- 
cal planes to pass lengthwise, cutting it in the lines in which the 
side-slopes meet the base of the road, (which is the bottom of an 
excavation, or the top of an embankment) as the lines CG and 
DH, of Fig. 128. These planes divide the prismoid into a cen- 
tral prism, and two pyramids or frusta. The content of the entire 
prismoid is expressed, according to formula [G], page 358, by 

{2s{g-\-hf-\-U{g + h)-2sgh]X^ [G] 

This may be decomposed into these two portions : 

[35(5-FA)]xl = |(--fA) [K] 

[2s{g-\-hy-2sgh-\xL = f^[ig + hy-gh] . . . [L] 

Formula [K] expresses the content of the central prism, and for- 
mula [L] that of the two pyramids or frusta. Denoting the end 
depths (without regarding which is the greater) by h and h', (the 
former representing the depth at the starting point, and the latter 
that at the farther end) the formulae become 

|(A+A') [M] 

£[{h-\-h'Y — hh'] . . . [N] 

Considering now the next prismoid, or following length of exca- 
vation, (or embankment) its first depth is seen to be identical with 
the last depth of the preceding prismoid, i. e. it is A'. Calling the 



APPENDIX. 361 

depth at its farther end A", the content of its central prism, by 
formula [M], will be 

— {h! + h") 

The content of the third length will similarly be 

^(A" + A"') 

and so on for the succeeding portions, I being the same in each. 
The sum of any number of these will be 

%■ {{h + h') + (A' + h") + (A" + in + &c ] 

= — (7i + 2h' + 2h" + 2A'" + &c.) 

Designating the last depth of the series by H, this expression 
may be written 

II ^A -{- A' + h" + h'" + Ai'^ + &c +—).... [0] 

Expressed in words, it then gives this 

KULE. 

To find the cubical contents of the central prisms, add together 
half of the first and last depths, and all the intermediate depths. 
Multiply their sum by the breadth of base, and that product by the 
length in feet of one of the equal distances. The last product will 
be the contents in cubic feet. 

The content of the two pyramids or frusta, on each side of the 
central prism, is for the first length, by formula N, 

y[(A + A')=-M'] 

For the second length it is —[{h' + h"f — h'h"] 

For the third length it is — [{h" + A'")' — /i"A"'] ; and so on. 

For any number of equal lengths, the sum of the contents is 

'1 [^n + h'f + (h' + h'T + &c. — {hh' + h'h" + &c.)] . . . . [P] 



362 APPENDIX 

Expressed in words, it gives this 



RULE. 

To find the cubical content of the pyramids or frusta, square the 
£um of the first and second depths, the second and third, the third 
and fourth, and so on, and add these squares together. Multiply 
the first depth by the second, the second by the third, and so on, 
and add the products together. Subtract the sum of the products 
from the sum of the squares. Multiply the difference by the length 
in feet of one of the equal distances, and that product by the ratio 
of the side-slopes to unity. Divide the last product by three, and 
the quotient will be the content in cubic feet. 

The sum of the two contents, thus obtained by formulae [0] and 
[P], or by the Rules derived from them, will be the total content 
required. 

In the following example, the width of base is 30 feet, the side- 
slopes 2 to 1, and the equal distances, at which the levels were 
taken, are each 100 feet. Therefore h = 30, s = 2, I = 100, and 
h, A', A" =■ the successive numbers in the third column of the table. 
In substituting the values of the quantities in the formula; they will 
be more conveniently vi/ritten under each other. 



Station. 


Distance. 


Depth. 


I 




= A 


2 


100 


2. = A' 


3 


100 


4. = h" 


4 


100 


3. =z A'" 


5 


100 


5. =:AV 


6 


100 


1. r=Av 


7 


100 


4. ==H 



The content of the central prism, by formula [O], = 
0. 



30 X 100 X -^ 



+ 2 
+ 4 

1" ? t = 30 X 100 X 17 . =: 51000 . cubic feet. 
+ 5 



+ 1 
+ _2 

L 17 J 



APPENDIX. 



363 



The contents of the pyramids and frusta, by formula [P], 



2X 100 



X < 



(0+2)^1 
+ (2 + 4)= 
+ (4 + 3^ 
+ (3 + 5)^ 
+ (5 + 1)= 
+ (1 + 4)= 





r 2X 41 






+ 4X3 






+ 3X5 
+ 5X1 
.+ 1X4. 


> 







+ 36 




r 1 

8 




200 




+ 49 




+ 12 






+ 64 


— 


+ 15 


I 


3 




+ 36 
+ 25 




+ 5 
+ 4 






. 


^ 214^ 




^ 44^ 


_ 



y—^X 170=11333. 



51000+ 11333. =62333 cubic feet = 2308.6 cubic yards 
the entire cubical content required. 



TABLES 

FOE CALCULATING EXCAVATION AND EMBANKMENT. 

The Tables at the end of this volume are extracted from those 
of Sir John Macneill, referred to on page 356. The numerals at 
the top and side of each table represent the depths or heights of 
the cutting or filling at its ends. The numbers in the body of the 
table indicate the number of cubic yards for the corresponding 
depths, and for a longitudinal distance of 1 foot. Thus, if the 
slopes of a given cutting be 1^ to l,the base 20 feet, the depths at 
the two ends 2 and 5 feet, and the distance between them 100 feet, 
find in Table I. the numeral 2 in the side column ; follow out the 
horizontal line corresponding to it till it meets the vertical column 
under the numeral 5 in the top line. At the intersection is 3.31, 
the cubic yards for a distance of 1 foot. Multiply this by 100, and 
the product is the number of cubic yards required. 

The use of such Tables is limited by the inconvenience of 
making them voluminous enough to embrace every variety of slope, 
base, and depths, (though the fractional numbers wanting may be 
interpolated) but in the cases to which they apply, they unite the 
advantages of greatly lessened labor, and increased accuracy. 



364 APPENDIX. 



4. CALCULATION BY MEAN PROPORTIONALS. 

A fourth method, called that of " Mean proportionals," is some- 
times, though very improperly,employed. It assumes implicitly that 
the mass is a frustum of a pyramid, i. e. that all its sides, if pro- 
duced, M'ould intersect in one vertex, a supposition which would 
very seldom be perfectly true. On this assumption the following 
is the Rule. 

Add together the areas of the two ends, and a mean proportional 
between them, (found by extracting the square root of their product) 
and multiply the sum of these three areas by the length of the 
frustum, and divide the product by three. The result is always 
much less than the truths for it treats as pyramids, or thirds of 
prisms, the wedge-shaped pieces which are really halves of prisms. 
It is farthest from the truth when one of the areas = 0. 

5. IRREGULAR CROSS-SECTIONS. 

The cross-section of the ground, ^t right angles to the direction 
of the road, has been assumed to be level. But the height of the 
surface of the ground usually varies considerably within the width 
to be occupied by the future road, and renders necessary the taking 
of levels not merely on the centre line, but also on the sides at the 
points in which the side-slopes, of the cuttings or fillings of the road, 
would intersect the surface of the ground. Other intermediate lev- 
els are also sometimes required. 

The height of the ground above the grade line of the road on the 
centre line is called the " centre cutting ;" and the heights at the 
intersection of the side-slopes of the cuttings with the ground on 
each side of any station are called the "right cutting" and " left 
cutting ;" abbreviated into C. C R. C L. C. 

In embankments, the corresponding heights are called " centre 

bank," "right bank," and "left bank;" usually written C. B 

R. B L. B. 

For greater accuracy, these cross-sections should be taken at 
every chain or less. If an abrupt change in the level of the ground 
requires a levelling between these regular stations, it is called an 
" intermediate" one. 

The following table presents various examples of irregular cross- 



APPENDIX. 



365 



sections. The slopes are assumed to be 2 to 1, and the width of 
the road to be 20 feet. 









1 










End Areas 


Station. 


Distance. 


L. C. 


c. c. 



K.V. 




L. B. 


C. B. 


R. B. 


Excavation. 


Eml)anl<nient. 


1 
















2 


100 


2.0 


2.0 


2.0 








48. 




3 


100 


3.0 


2.6 


3.4 








74.64 




4 


100 


3.0 




2.0 








62. 




Inter. 


CO 


1.0 

















5. 





5 


40 

















2.0 





10. 


6 


100 








3.0 


4.0 


6.0 




121. 


7 


100 























We will proceed to sketch and note each cross-section, writing 
each height vertically in its appropriate place, and show how its 
area is obtained by dividing it into triangles, of which the base and 
height are known. 

At station 1 the cutting begins, with an area = 0. 
Fiff. 149. 



4. X 20. X 4. 

At station 2, Fig. 149, the section is of uniform depth, and its area 
is simply (20 + 2 X 2) X 2.0 = 48. 



Fhr. 150. 




6. X 10. X 

At station 3, Fig. 150, the lower left-hand triangle = 



The lower right-hand triangle = 



The two remaining triangles = 



10 X 3.4 



= 17. 



2.6X (6-f 10+10-F6.8) 



42.04 



The entire area therefore 

24 



= 74.64 



366 




At station 4, only two levels were thought necessary, viz. those 
of the outside cuttings, without the centre one. To find the area, 
consider the figure as a trapezoid, minus the right-angled triangles 
at each end. 

(6 + 20 -f 4) X ?ll-^ = 75. 



Trapezoid 
Left-hand triangle 
Right-hand triangle 



6X3 



2 
4X2 



= —4 



— 13 



— 13. 

- 62. 



Area of cross-section, 

A simple algebraic expression for this area may be found thus : 
call the breadth of base b, the outside cuttings d and e, the ratio of 
side-slopes to unity s. The area will be 
(b + sd+ se) (d + e) _ sd' se' 
2 



2 



2 



■■ h — 1- sde. 



The above example would then be 20 X --f 2X3X2 = 



50 + 



12 = 62. 



Fig. 152. 



10. X 10. 

Between stations 4 and 5, at 60 feet from the former, an interme- 
diate cross-section was made necessary, by the cutting " running 
out" on one side. The area, Fig. 152, is only the single triangle 
1 X 1 -0 _. 
2 ~ 

At station 5, 40 feet farther, the cutting entirely runs out, and its 
area at that point becomes 0. The embankment had commenced. 



APPENDIX. 
Fiff. 153. 



367 




with area 0, at the preceding intermediate station, and at this sta- 

10. 



„ . 10 X 2 

tion Its area, r ig. 153, is — - — 



At station 0, the cross-section resembles that at station 3, in- 
Fig. 154. 
6 X 10. 




verted, and is calculated in the same manner by division into 
triangles, as is shown in Fig. 154. 

10 X 3 



Left-hand triangle 
Rijrht-hand triangle - = 



2 
10 X 6 



= 15. 
= 30. 



rp ■ • . • 1 4X (6+1 0+10 + 12) 

1 wo remaming triangles = = 7d. 

Entire area, . . . - = 121. 

At station 7, the embankment runs out, and the area = 0. 



MEAN HEIGHTS. 

To apply the prismoidal formula to cases of irregular cross-sec- 
tions, it is necessary to calculate the mean heights of these cross- 
sections, to be subsequently averaged together to find the middle 
height; which produces the middle area. The following problem is 
therefore to be solved : Given the area of any irregular section, re- 
quired the mean height which would produce the same area, the 
base and slopes remaining the same. 



368 



APPENDIX. 



Fig. 155. 
b 





Let a represent the given area ; b the breadth of base, or road- 
bed ; s, the ratio of side-slopes to unity ; and oc the mean height 
required. 

Then a ^sx"^ -{- hx ; by solving which equation we obtain 

In all the preceding examples, — = 

At station 3, (p. 365) a = 74.6 .-.x — ^ { 



= 5. 

74.6 



\ 2 



+ 5'M -5 = 



V'62.3 — 5 = 7.89 — 5 = 2.89. If this mean height be verified, it 
will be found to produce the original area. Thus substituting it in the 
above expression for a, we obtain 2 X 2.89'^ + 20 X 2.89= 74.6. 

A similar process will give the mean heights for the remaining 
cross-sections. They may then be employed, as were the uniform 
heights in the original examples, to find the middle heights, and 
thence the middle areas required by the prismoidal formula; or 
as the values of g and h in the easier formulae, which have been 
therefrom deduced. 

In most cases, it will be sufficiently accurate to take only three 
levels, viz. at the centre, and at the foot, or top, of each side slope. 
The " equivalent mean height" can then be at once obtained by the 
following easy formula, in which c ^ the cut or fill at the centre, 
and p and q the outside cuttings or fillings : 

y/ (s'p->rsq'^b) {b-\-2sc) — b 

^ = 27 • 

When the " distances out" are given, calling them d and d', we have 

\/{d-\-d') {b-\-2sc) — b 

X = — . 

2s 

In Sidelong ground, as in Fig. 151, if the level in the centre be 

used as if the ground was level, the resulting area will be too small 

(in Fig. 151, = 61.5) ; if the mean of the two extreme levels be ta- 

ken, the result will be too great (in Fig. 151, = 62.5). 









TABLE I.— SLOPES 1^ to 1.— BASE 20. 












1 


3 


3 


4 


5 


6 


7 


8 


9 


10 


a 

(D 






f^ 






















Ui 









0.39 


0.81 


1.28 


1.78 


2.31 


2.89 


3.50 


4.15 


4.83 


5.55 









1 


0.80 


1.24 


1.72 


2.24 


2.80 


3.39 


4.02 


4.68 


5.39 


6.13 


1 








2 


1.-24 


1.70 


2.20 


2.74 


3.31 


3.92 


4.57 


5.26 


5.98 


6.74 


2 E 








3 


1.72 


2.20 


2.72 


3.28 


3.87 


4.50 


5.17 


5.87 


6.61 


7.39 


3 








4 


2.24 


2.74 


3.28 


3.85 


4.46 


5.11 


5.80 


6.52 


7.28 


8.07 


4 








5 


2.80 


3.31 


3.87 


4.46 


5.09 


5.76 


6.40 


7.20 


7.98 


8.80 


5 

6 1 








6 


3.39 


3.92 


4.50 


5.11 


5.76 


6.44 


7.17 


7.92 


8.72 


9.55 








7 


.4.02 


4.57 


5.17 


5.80 


6.46 


7.17 


7.91 


8.68 


9.50 


10.35 


1 t 








8 


4.G8 


5.21) 


5.87 


6.52 


7.20 


7.92 


8.68 


9.48 


10.31 


11.18 


8 








9 


5.39 


5.98 


6.61 


7.28 


7.98 


8.72 


9.50 


10.31 


11.16 


12.05 


9 








10 


0.13 


6.74 


7.39 


8.07 


8.80 


9.55 


10.35 


11.18 


12.05 


12.96 


10 








11 


6.91 


7.54 


8.20 


8.91 


9.05 


10.42 


11.24 


12.09 


12.98 


13.91 


11 








12 


7.72 


8.37 


9.05 


9.78 


10.54 


11.33 


12.17 


13.04 


13.94 


14.89 


12 








r.i 


8.57 


9.24 


9.94 


10.68 


11.46 


12.28 


13.13 


14.02 


14.94 


15.91 


13 1 






14 


9.40 


10.15 


10.87 


11.63 


12.42 


13.26 


14.13 


15.04 


15.98 


16.90 


14 








15 


10.39 


11.09 


11.83 


12.61 


13.42 


14.28 


15.17 


16.09 


17.05 


18.05 


15 1 






16 


11.35 


12.07 


12 83 


13.63 


14.46 


15.33 


10.24 


17.18 


18.16 


19.18 


16 1 






17 


12.35 


13.09 


13.87 


14.68 


15.54 


16.42 


17.35 


18.31 


19.31 


20.35 


17 








18 


13.39 


14.13 


14.94 


15.78 


16.65 


17.55 


13.50 


19.48 


20.. 50 


21 . 55 


IS 








1<J 


14.40 


15.24 


16.05 


16.91 


17.80 


18.72 


19.08 


20.68 


21.72 


22.80 


19 








i>0 


15.57 


10.37 


17.20 


18.07 


18.98 


19.92 


20.91 


21.92 


22.98 


24.07 


20 






I 


2 


3 


4 


5 


6 


7 


8 


9 


10 






% 


11 


12 


13 


U 


15 


16 


17 


IR 


19 


20 


■£ 








f^ 
































G.31 


7.11 


7.94 


8.81 


9.72 


10.67 


11.65 


12.67 


13.72 


14.81 






1 


G.91 


7.72 


8.5- 


9.46 


10.39 


11.35 


12.35 


13.39 


14.46 


15.57 


1 








2 


7.54 


8.37 


9.2. 


10.15 


11.09 


12.07 


13.09 


14.15 


15.24 


16.37 


2 








3 


8.20 


9.05 


9.9' 


10.87 


11.83 


12.82 


13.87 


14.94 


16.05 


17.20 


3 








4 


8.91 


9.78 


10.68 11.63 


12.61 


13.63 


14. C8 


15.78 


16.91 


18.07 


4 






o 


9.65 


10.54 


11.46 12.42 


13.42 


14.40 


15.54 


16.65 


17.80 


18.98 


5 








6 


10.42 


11.33 


12.28 13.26 


14.28 


15.33 


10.42 


17.55 


18.72 


19.92 


6 








7 


11.24 


12.17 


13.13 14.13 


15.17 


16.24 


17.35 


18.50 


19.68 


20.91 


7 








8 


12.09 


13.04 


14.02 15.04 


16.09 


17.18 


18.31 


19.48 


20.68 


21.92 


8 








9 


12.98 


13.9-i 


14.94 15.98 


17.05 


18.16 


19.31 


20.50 


21.72 


22.08 


9 








10 


13.91 


14.89 


15.9l| 16.96 


18.05 


19.18 


20.35 


21.55 


22.80 


24.07 


10 








11 


14.87 


15.87 


16.91 17.98 


19.09 


20.24 


21.42 


22.05 


23.91 


25.20 


11 






i-Z 


15.87 


16. 8c 


17.94 19.03 


20.17 


21. 3£ 


22.54 


23.78 


25.05 


26.37 


12 








13 


16.91 


17.94 


19.02 20.13 


21.28 


22.46 


23.68 


24.94 


20.24 


27.57 


13 








14 


17.88 


19.03 


20.13 21.26 


22.42 


23.63 


24.87 


26.15 


27.46 


28.81 


14 








15 


19.09 


20.17 


21.28 22.42 

1 


23.61 


24.83 


26.09 


27.39 


28.72 


30.09 


15 








1 IG 


20.24 


21.33 


22. 46^ 23.63 


24.83 


26.07 


27.35 


28.67 


30.02 


31.41 


16 








18 


21.42 


22.54 


23.68 24.87 


26.09 


27.35 


28.6,") 


29.98 


31.35 


.32.76 


17 








22.65 


23 . 78 


24.94 26.15 


27. 3t 


28.67 


29. G8 


31.33 


32.72 


34.15 


18 






19 


23.91 


25.05 


26.24 27.46 


28.72 


30.02 


31.35 


,32.72 


34.13 


35 . 57 


19 






i 


iiO 


25.20 


26.37 


27.57 28.81 


30.09 


31.41 


32.76 


34.15 


35.57 


37.04 


20 








11 


12 


13 14 


15 


16 


17 


18 


19 


20 




1 
j 


^ 














S69 







TABLE I.— SLOPES U to 1.— BASE 30. 



"7 


1 


2 


.s 


4 5 


6 


7 


8 


9 


10 


« 


fi 






















f» 





0.57 


1.19 


1.83 


2.52 


3.24 


4.00 


4.80 


5.63 


6.49 


7.41 





1 


1.17 


1.80 


2.46 


3.17 


3.91 


4.69 


5.. 50 


6.35 


7.24 


8.n 


1 


2 


1.80 


2.44 


3.13 


3.85 


4.61 


5.41 


6.24 


7.11 


8.02 


8.96 


o 


3 


2.46 


3.13 


3.83 


4.57 


5.35 


6.17 


7.02 


7.91 


8.83 


9.80 


3 


4 


3.17 


3.85 


4.57 


5.33 


6.13 


6.96 


7.83 


8.74 


9.69 


10.67 


4 


5 


3.91 


4.61 


5.35 


G.13 


6.94 


7.80 


8.69 


9.61 


10.57 


11.57 


5 


G 


4.69 


5.41 


6.17 


6.96 


7.811 


S.67 


9.57 


10.52 


11.50 


12.521 G 1 


7 


5.50 


6.24 


7.02 


7.83 


8.1)9 


9.57 


10.50 


11.46 


12.46 


13.5fll 7 


8 


(i.35 


7.11 


7.91 


8.74 


9.61 


10.52 


11.46 


12.44 


13.46 


14.52, 8 I 


9 


7.24 


8.02 


8.83 


9.69 


10.57 


11.50 


12.46 


13.46 


14.50 


15.57 


9 


10 


8.17 


8.96 


9.80 


10.67 


11.57 


12.52 


13.50 


14.52 


15.57 


16. C7 


10 


11 


9.13 


9.94 


10.80 


11.69 


12.61 


13.57 


14.57 


15.61 


16.69 


17.80 


II 


1-2 


10.13 


10.96 


11.83 


12.74 


13.69 


14.67 


15.69 


16.74 


17.83 


18.96 


12 


13 


11.17 


12.02 


12.01 


13.82 


14.80 


15.80 


16.83 


17.91 


19.02 


20.17 


13 


14 


li.24 


13.11 


14.02 


14.96 


15.94 


16.96 


18.02 


19.11 


20.24 


21.41 


14 


15 


13.35 


14.24 


15.17 


16.13 


17.13 


18.17 


19.24 


20.35 


21.50 


22.69 


15 


IG 


14.50 


15.41 


16.35 


17.33 


18.35 


19.41 


20.50 


21.63 


22.80 


24.00 


16 


17 


15.69 


16.61 


17.57 


18.57 


19.61 


20.69 


21.80 


22.94 


24.13 


25.35 


17 


lb 


1G.91 


J7.85 


18.8: 


19.85 


20.91 


22.00 


23.1.; 


24.3(1 


25.50 


26.74 


18 


19 


18.17 


19.13 


20.13 


21.17 


22 . 2- 


23.. 35 


24 . 50 


25.69 


26.91 


28.17 


19 


iiU 


19.46 


20.44 


21.46 


22 . 5- 


23.61 


24.74 


25.91 


27. IJ 


28.35 


29.63 


20 




1 


2 


3 


4 


5 


6 


7 


8 


9 


lU 

































"-"""*""- 


•"■"* — "■•' 


— '"■.•■-^ ->■■•■'■■ 


,.,Ui„^.r-» 




■^'-'-"" — -^ 




■^•-■•''•'"■•'- 


"■- ""-^ 


■**-— — .— jbi-^jjiitiay 


y *.> 






















■^ R 


1 <u 


11 


12 


13 


14 


]^ 


1(1 


17 


18 


U) 


20 


<u 1 


a ^ 






















1 


1 


8.35 


9.33 


10.35 


11.41 


12.50 


13.63 


14.80 


16.00 


17.24 


18.52 


1 1 


9.13 


10.13 


11.17 


12.24 


13.35 


14.50 


15.69 


16.91 


18.17 


19.46 


1 1 


1 2 


9.94 


10.96 


12.02 


13.11 


14.24 


15.41 


16.61 


17.85 


19.13 


20.44 


2 j 


i ^ 


10.80 


11.83 


12.91 


14.02 


15.17 


16. .35 


17.57 


18.83 


20.13 


21.46 


3 


4 


11.69 


12.74 


13.83 


14.96 


16.13 


17.33 


18.57 


19.85 


21.17 


22.52 


4 


5 


12.61 


13.69 


14.80 


15.94 


17.13 


18.35 


19.61 


20.91 


22 . 24 


23.61 


5 



6 


13.57 


14.67 


15.80 


16.96 


18.17 


19.41 


20.69 


22.00 


23.35 


24.74 




14.57 


15.69 


16.83 


18.02 


19.24 


20.50 


21.80 


23.13 


24.50 


25.91 


7 


8 


15.61 


16.74 


17.91 


19.11 


20.35 


21.63 


22.94 


24.30 


25.69 


27.11 


8 


9 


16.69 


17.83 


19.02 


20.24 


21.50 


22.80 


24.13 


25.50 


26.91 


28.35 


9 


10 


17.80 


18.96 


20.17 


21.41 


22.69 


24.00 


25.35 


26.74 


28.17 


29.63 


10 


11 


18.94 


20.13 


21.35 


22.61 


23.91 


25.24 


26.61 


28.02 


29.46 


30.94 


11 


12 


20.13 


21.. 33 


22.57 


23.85 


25.17 


26.52 


27.91 


29.33 


30.80 


32.. 30 


12 1 


13 


21.35 


22.57 


23.83 


25.13 


26.46 


27.83 


29.24 


30 . 69 


.32.17 


33.69 


13 


14 


22.61 


23.85 


25.13 


26.44 


27.80 


29.19 


.30.61 


.32.07 


33.57 


35.11 


14 


15 


23.91 


25.17 


26.46 


27.80 


29.17 


30.57 


32.02 


33.50 


35.02 


36.57 


15 


16 


25.24 


26.52 


27.83 


29.19 


.30.57 


32.00 


33.46 


34.96 


36.50 


.38.07 


16 


17 


26.61 


27.91 


29.24 


30.61 


32.02 


33.46 


34.98 


31). 46 


.38.02 


39.61 


17 


18 


28.02 


29.33 


30.69 


32.07 


33.. iO 


34.96 


36.46 


.38.00 


39.. 57 


41.19 


18 


19 


29.46 


30.80 


32.17 


33.57 


35.02 


.36.50 


38.02 


39.. 57 


41.17 


42.80 


19 


20 


30.94 


.32.30 


33. C9 


35.11 


36.57 


.38.07 


39.61 


41.19 


42.80 


44.44 


20 


BSd 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


J 



S70 



TABLE III.— SLOPES 2 to 1.— BASE 20. 





■"•""^ 


ESEBaa 


'^'^"■^-' 








1.1 




1 


9, 


3 


4 


5 


6 


7 


8 


n 


10 


<u 1 






















Pm g 


1 


0.40 


0.84 


1.33 


1.88 


2.47 


3.31 


3.80 


4.54 


5.33 


G.17 


1 


1 I 


0.81 


1.28 


1.8U 


2.37 


2.99 


3.65 


4.37 


5.13 


5.95 


6.81 


1 1 




1.28 


1.78 


2.32 


2.91 


3.55 


4.25 


4.99 


5.78 


6.62 


7.51 


o 


3 


1.80 


2.32 


2.89 


3.51 


4.17 


4.89 


5.65 


6.47 


7.33 


8.25 


3 I 


4 


2.37 


2.91 


3.51 


4.15 


4.84 


5.58 


6.37 


7.21 


8.10 


9.04 


4 ! 

5 


5 


2.99 


3.55 


4.17 


4.84 


5.55 


6.. 32 


7.13 


8.00 


8.91 


9.88 


fi 


3.C5 


4.25 


4.89 


5.58 


6.32 


7.11 


7.95 


8.84 


9.78 


10.76 


c 


7 


4.37 


4.99 


5.65 


6.37 


7.13 


7.95 


8.81 


9.73 


10.69 


11.70 


7 


8 


5.13 


5.78 


6.47 


7.21 


8.00 


8.84 


9.73 


10.67 


11.65 


12.09 


S 


9 


5.95 


6.62 


7.33 


8.10 


8.91 


9.78 


10.69 


11.65 


.12.67 


13.73 


S i 


10 


6.81 


7.51 


8.25 


9.04 


9.88 


10.76 


11.70 


12.69 


13.73 


14.81 


10 1 


11 


7.73 


8.44 


9.21 


10.02 


10.89 


11.80 


12.76 


13.78 


14.84 


15.95 


11 1 


12 


8.69 


9.43 


10.22 


11.06 


11.95 


12.89 


13.88 


14.91 


16.00 


17.13 


12 g 


13 


9.70 


10.47 


11.28 


12.15 


13.06 


14.02 


15.04 


16.10 


17.21 


18.37 


13 
14 


14 


10.76 


11.55 


12.39 


13.28 


14.22 


15.21 


16.25 


17.33 


18.47 


19.65 


15 


11.88 


12.69 


13.55 


14.47 


15.43 


16.44 


17.51 


18.62 


19.78 


20.99 


15 


16 


13.04 


13.88 


14.76 


1.5.70 


16.69 


17.73 


18.81 


19.95 


21.13 


22.37 


16 


17 


14.25 


15.11 


16.02 


16.99 


18.00 


19.06 


20.17 


21.33 


22.54 


23.80 


17 I 


It 


15.51 


1G.39 


17. 3^ 


18.32 


19.36 


20.44 


21.58 


22.76 


24.00 


25.28 


18 1 


19 


16.81 


17.73 


18.69 


19.70 


20.77 


21.88 


23.04 


24.25 


25. 5J 


26.81 


19 


20 


18.17 


19.11 


20.10 


21.13 


22 22 


23.36 


24.54 


25.78 


27.06 


28.40 


20 1 




1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


\ 



nr 


















'■'-''■'■'■ 


""^'^"""'Xl 




11 


1'^ 


13 


14 


15 


IH 


17 


IH 


1!) 


20 S 1 


i h 




















17.28 ! 


1 " 


7.06 


8.00 


8.99 


10.02 


11.11 


12.25 


13.43 


14.67 


15.95 


1 


7.73 


8 69 


9.70 


10.76 


11.88 


13.04 


14.25 


15.51 


16.81 


18.17 1 


2 


8.44 


9.43 


10.47 


11.55 


12.09 


13.88 


15.11 


16.39 


17.73 


19.11 2 


3 


9.21 


10.22 


11.28 


12.39 


13.55 


14.70 


16.02 


17.33 


18.69 


20.10 3 
21.13 4 


4 


10.02 


11.07 


12.15 


13.28 


14.47 


15.70 


16.99 


18.32 


19.70 


o 


10.89 


11.95 


13.06 


14.22 


15.43 


16.69 


18.00 


19.36 


20.77 


22.22 


5 1 


1 6 


11.80 


12.89 


14. C2 


15.21 


16.44 


17.73 


19.06 


20.44 


21.88 


23.38 


6 1 


i ''' 


12.77 


13.88 


15.04 


16.25 


17.51 


18.81 


20.17 


21.58 


23.04 


24.54 


7 i 


1 ^ 


13.78 


14.91 


16.10 


17.33 


18.62 


19.95 


21.33 


22.76 


24.25 


25.78 


8 i 


9 


14.84 


16.00 


17.21 


18.47 


19.78 


21.13 


22.54 


24.00 


25.51 


27.06 


9 ^ 


10 


15.95 


17.13 


18.37 


19.65 


20.99 


22.37 


23.80 


25.28 


26.81 


28.40 


10 B 


11 


17.11 


18.32 


19.58 


20.89 


22.25 


23.65 


25.11 


26.62 


28.17 


29.78 


11 1 


12 


18.32 


19.55 


20.84 


22.17 


23.55 


24.99 


26.47 


28.00 


29.58 


31.21 


12 1 


13 


19.. 58 


20.84 


22.15 


23.51 


24.91 


26.37 


27.88 


29.43 


31.04 


32.09 


13 1 


i 14 


20.89 


22 17 


23.51 


24.89 


26.32 


27.80 


29.33 


30.91 


32.54 


34.22 


14 1 


1 ^^ 


22.25 


23.55 


24.91 


26.32 


27.78 


29.28 


30.84 


32.44 


34.10 


35.80 


15 1 


16 


23.65 


24.99 


26.37 


27.80 


29.28 


.30.81 


32.39 


34.02 


35.70 


37.43 


16 1 


17 


25.11 


26.47 


27.88 


29.33 


30.84 


32.39 


34.00 


35.65 


37.30 


39.11 


17 i 


18 


26.62 


28.00 


29.43 


30.91 


32.44 


34.02 


35.65 


37.33 


39.06 


40.84 


18 ^ 


19 


28.17 


29.58 


31.04 


32.54 


34.10 


35.70 


37.36 


39.06 


40.81 


42.62 


19 i 


20 


29.78 


31.21 


32.69 


34.22 


.35.80 


37.43 


39.11 


40.84 


42.62 


44.44 


20 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 





371 





TABLE IV.— SLOPES 2 to 1.- 


-BASE 30 


, 








a 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 









0.58 


1.21 


1.89 


2.62 


3.40 


4.22 


5.10 


6.02 


7.00 


8.02 







1 


1.18 


1.84 


2.54 


3.30 


4.10 


4.95 


5.85 


6.80 


7.80 


8.85 


1 






2 


1.84 


2.52 


3.25 


4.02 


4.85 


5.73 


6.65 


7.63 


8.05 


9 73 


2 






3 


2.54 


3.25 


4.00 


4.80 


5.65 


6.55 


7.51 


8.51 


9.55 


10.65 


3 ! 1 




4 
5 


3.30 


4.02 


4.80 


5.63 


6.51 


7.43 


8.41 


9.43 


30.51 


3 1 . 03 


4 






4.10 


4.85 


5.65 


6.51 


7.41 


8.36 


9.36 


10.41 


11.51 


12.65 


5 






6 


4.95 


5.73 


6.55 


7.43 


8.36 


9.33 


10.36 


11.43 


12.55 


13.73 


G 




i 1 7 


5.85 


6.65 


7.51 


8.41 


9.36 


10.36 


11.41 


12.51 


13.65 


14.85 


7 




1 is 


6.80 


7.63 


8.51 


9.43 


10.41 


11.43 


12.51 


13.63 


14. 8() 


10.02 


8 


1 


9 


7.80 


8.65 


9.55 


10. 5J 


11.51 


12.55 


13.65 


14.80 


16.00 


17.25 




I 


1 
1 


10 


8.85 


9.73 


10.65 


11.63 


12.65 


13.73 


14.85 


16.02 


17.25 


18.52 


10 






11 


9.95 


10.85 


11.80 


12.80 


13.85 


14.95 


16.10 


17.29 


18.54 


19.84 


11 






ti 


11.10 


12.02 


13.00 


14.02 


15.10 


16.22 


17.39 


18.62 


19.89 


21.21 


1'> 






13 


12.30 


13.25 


14.25 


15.30 


16.40 


17.54 


18.74 


19.99 


23.28 


22.03 


13 




1 


14 


13.54 


14.52 


15.54 


16.62 


17.74 


18.91 


20.13 


21.41 


22.73 


24.10 


14 




! 


15 


14.84 


15.84 


16.89 


17.99 


19.13 


20.33 


21.58 


22.88 


24.22 


25.62 


15 






16 


16.38 


17.21 


18.28 


19.41 


20.58 


21.80 


23.0^7 


24.39 


25.76 


27.38 


16 






17 


17.58 


18.63 


39.73 


20.88 


22.07 


23.32 


24.02 


25.96 


27.36 


28.80 


17 


' 


18 


19.02 


20.10 


21.22 


22.39 


23.62 


24.89 


26.21 


27.58 


29.00 


30.47 


18 


' 


19 


20.52 


21.62 


22.76 


23.96 


25.21 


26.51 


27.85 


29.25 


30.69 


32.18 


19 






iiO 


22.06 


23.18 


24.36 


25.58 


26.85 


28.17 


29.54 


30.96 


32.43 


33.95 


29 








1 


2 


3 


4 


5 


6 


7 


8 


9 


10 
















■" ""■" 






! 


(p 


11 


12 


13 


14 


15 


16 


n 


18 


19 


90 




: '^ 






















fe 









9.10 


10.22 


11.40 


12.02 


13.89 


15.21 


16.58 


18.00 


19.47 


20.99 









1 


9.95 


11.10 


13.30 


13.54 


14.84 


16.18 


17.58 


19.02 


20.52 


22.06 


1 




1 


2 


10.85 


12.02 


13.25 


14.52 


15.84 


17.21 


18.63 


20.10 


21.62 


23.18 






3 


11.80 


13.00 


14.25 


15.54 


16.89 


18.28 


19.73 


21.22 


22 76 


24.36 


3 






4 


12.80 


14.02 


15.30 


16.62 


17.99 


19.41 


20.88 


22.39 


23.96 


25.58 


4 






5 


13.85 


15.10 


16.40 


17.74 


19.13 


20.58 


22.07 


23.62 


25.21 


26.85 


5 






6 


14.95 


16.22 


17.54 


18.91 


20.33 


21.80 


23.32 


24.89 


20.51 


28.17 


6 




7 


16.10 


17.39 


18.74 


20.13 


21.58 


23.07 


24.62 


26.21 


27.85 


29.54 


7 




' 


8 


17.29 


18.62 


19.99 


21.41 


22.88 


24.39 


25.96 


27.58 


29.25 


30.96 


R 






9 


18.54 


19.89 


21.28 


22.73 


24.22 


25.76 


27.36 


29.00 


30.69 


32.43 


9 






10 


19.84 


21.21 


22.63 


24.10 


25.62 


27.18 


28.80 


30.47 


32.18 


33.95 


10 






11 


21.18 


22.58 


24.02 


25.52 


27.06 


28.65 


30.30 


31.99 


33.73 


35.. 52 


11 






I'i 


22.58 


24.00 


25.47 


26.99 


28.55 


30.17 


31.84 


33.55 


35., 32 


37.33 


32 




' 


13 


24.02 


25.47 


26.96 


28. 5J 


30.10 


3 J. 74 


33.43 


35.17 


36.96 


38.80 


13 




1 


14 


25.52 


26.99 


28,51 


30.07 


31.69 


33.36 


35.07 


36.84 


38.65 


40.. 'i2 


14 






15 


26.00 


28.55 


30.10 


31.09 


33.. 33 


35.02 


30.76 


38.55 


40.39 


42.28 


15 






16 


28.65 


30.17 


31.74 


33.36 


35.02 


36 . 74 


.38.51 


40.32 


42.18 


44.10 


16 






J7 


30.30 


3]. 84 


33.43 


35.07 


36.76 


3-8.51 


40.30 


42; 13 


44. B2 


45.96 


17 






18 


31. 9B 


33.55 


35.17 


36.84 


38.55 


40.32 


42.13 


44.00 


45.91 


47.88 


18 




1 


19 


.33.73 


35.32 


36.96 


38.65 


40.39 


42.18' 44.92 


45.91 


47.85 


49.84 


19 




( 

1 
1 


.0 


35 . 52 


37.13 


38.80 


40.53 


42.28 


44.10 


45. SO 


47.88 


49.84 


51.85 
20 


20 




1 
11 


12 


13 


14 


15 


16 


17 


18 


19 


1 
i 
















872 






















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